The nettle was grasped; early in 1968 a White Paper was published, a bill soon followed. But in the face of every kind of obstruction in the Commons from an unlikely coalition of right-wing Conservatives and left- wing Labour, Wilson let the nettle drop. By April 1969, the issue was effectively dead.
Lord Lester, now a leading constitutional lawyer and then adviser to Roy Jenkins, can see how history could repeat itself, through a lack of will, under an incoming Blair government.
"It would be terribly easy for constitutional reform to suffer a similar fate next time, unless it is taken as seriously as the Thatcherites took their mission of breaking trade union and local government power, and privatising public services," he cautions.
Drifting in the right direction, but making no policy commitments, might work for a minimum wage, but it is not good enough for a major constitutional reform which undermines the British social and political establishment. Whatever formula Labour reaches it must be constitutionally watertight so the Conservative peers cannot use their inbuilt majority to hold it up. It must produce a blueprint for something that will work in practice, or like Wilson's bill it will be blown apart in the detail.
Yet two years at most from an election, Labour is still speaking with many voices not only on exactly how to reform the Lords but, even more alarmingly, on just why it wants to do it. Does it want a stronger Lords, in case another Tory like Mrs Thatcher gets in? Or a weaker one in case its own legislation gets interfered with?
Graham Allen, MP for Nottingham North, was until recently the party's spokesman on the constitution, and perhaps uniquely among senior Labour figures he has thought through what he wants, from principle to detail. He probably still speaks for the biggest slice of the party activists.
In a pamphlet published earlier this year, Allen set out his agenda: "Labour's unfulfilled commitment to elect the second chamber was always seen as part of Labour's attempt to negate one of the worst aspects of privilege and class. Now there is also a positive reason to elect a second chamber in order that it can play a meaningful part as one of many legitimate political institutions within a pluralist democracy."
This would give the Lords a renewed legitimacy, challenging the Commons. Allen accepts the implication with an equanimity which must alarm Labour figures already day-dreaming of finally sitting behind those ministerial desks armed with executive power and at the head of a powerful machine. "The reality is that both chambers need to be freed from the executive and allowed to express themselves if we are to have a pluralist democracy," he argues.
Supporters of Allen's view, the idealistic-democratic wing of the party, bring to the debate a whole legislative shopping list, which threatens an even bigger nightmare for the Labour leadership. Lord Lester, an advocate of this position, a trustee of Charter 88 and now a Liberal Democrat, says: "We urgently need nothing less than a new constitutional settlement." Proportional representation, a Bill of Rights, devolution, and rejuvenated local government are inextricably linked, he believes. "The creation of a Scottish Parliament and regional assemblies and executives would profoundly alter the composition and functions of the Westminster Parliament and would influence the way in which the House of Lords was reformed."
These ultra-democrats represent one end of the spread of Labour opinion on Lords' reform. Significantly, Allen is no longer party spokesman on the subject. At the other end of the spectrum are those who want the Lords to become a giant quango. Supporters of the extreme form of this view would have the Lords entirely nominated by the party machines, starting from scratch, to reflect the political composition of the Commons.
Others in the party, including its last leader but three, Michael Foot, are apparently off the spectrum altogether. They would like the Lords simply to be abolished, arguing that the Commons could take on its role, by consulting more effectively on legislation, and treating the committee stage of legislation as a forum for debate rather than a sparring match. No serious figure in the existing Labour establishment expects this view to prevail. Lord McIntosh, deputy leader of the Labour Party in the Lords, still holds it, but acknowledges that he has lost the argument inside the new Labour Party and is keeping his head down.
Faced with such a spread of views, and a wide measure of indifference, Labour's policy on Lords reform will not emerge routinely, or by consensus: the decisions will rest with Tony Blair and with Jack Straw, the Home Affairs spokesman, a radical opponent of the hereditary principle, but a pragmatist who knows Labour must balance legislation on such abstract matters as constitutional reform with action on issues like health and education which are matters of more immediate public concern. This sense of pragmatism is reflected in the choice of Kim Howells as the new Labour spokesman on the constitution, not because he has a deep knowledge or interest in it, but because he too is a pragmatist, and because, on Lords' reform at least, "there is no difference between me and Jack."
Howells acknowledges the virtues of the present Lords: its broad expertise, the awesome ability of some members in select committees and the fact that its written reports are more erudite than those of Commons committees. So far his analysis of reform contains as many questions as answers; on the detail, when asked about his plans, he seems to be still only thinking aloud.
The only definite commitment so far is to abolish the voting rights of hereditary peers. But if you take away the rights of hereditary peers, he acknowledges, you would be still be left with a built-in political imbalance among the life peers, of whom an estimated 34 per cent are Conservatives and only 23 per cent Labour.
"We would still probably need new peers," Howells says. "If you wish to continue to get business through Parliament it will mean creating new ones. Part of this would be done by turning hereditary peers into life peers. Their tenure would have to be for life, and we would have to make them attend somehow.
"One possibility is a committee to nominate peers, something like a joint standing committee of both houses. There must be some method of making [the Lords] reflect the political balance." One thing ruled out is Lord Lester's constitutional shopping-list. "I'm opposed to constitutional reform all in one bill. We'd get into a mire of constitutional reform."
Howells believes the deliberations of the party between now and the election will find a way to preserve the virtues of the existing system while abolishing the hereditary element.
There are further difficulties probably not even envisaged yet by Labour, never mind solved, and even superficially esoteric points could act as a rallying call for opponents, and delay legislation for months.
For example, according to one senior Palace of Westminster official, if you stop hereditary peers attending as well as voting, it would be a major embarrassment to the Queen, because when she made them peers she formally issued the writ summoning them to "treat and give counsel". If you stop them attending, she has to withdraw her writ.
For that reason, if for no other, Labour may well find itself allowing hereditary peers to turn up but not vote in the knowledge that their successors will not receive a royal summons.
The same official's opinion is also that a firm manifesto commitment by Labour is essential to stop the Lords opposing and obstructing the process. Convention in the Lords has it that any bill which corresponds exactly to a manifesto pledge should not be opposed. That makes it more than just academic whether Labour forms a detailed policy soon.
Only in the past few weeks has the party machinery which turns ideas into policies started grinding into life. Howells and Straw recently held a meeting of a working group on Lords reform, comprising six interested Labour life peers, including at least one former minister. There was consensus on ends - abolish the hereditary principle, retain the expertise, but the discussion did not get much beyond that. The group will meet again soon.
Eventually the discussion will lead to a paper, written by Straw and Howells, going to the party's policy forum, its Commission on Democracy, a group of MPs and party apparatchiks. According to Howells this will happen before the summer recess. There may be other papers, expressing minority dissenting views, if the apparent consensus among the six peers dissolves when it comes to the detail.
After the Commission has opined, the formal steps at least will be laid out. A policy will then go to the shadow cabinet, and eventually to party conference (but almost certainly not this year's). Whatever results, it seems certain to be a considerable retreat from the 1993 conference, which backed election of the House of Lords on a regional basis and by proportional representation - and the leadership will have to work as hard as they did with Clause IV to explain the retreat to the troops.
Howells is aware of the enormous commitment Labour has already made for its first 100 days in office, and Lords' reform will certainly not be among them. What he will say is that Labour may act in the first two years, and he makes a firm commitment to remove the hereditary principle within the life of the first Parliament.
Howells and Straw no doubt agree with Graham Allen when he says: "One sizeable advantage of tackling the second chamber is that it will be highly symbolic of Labour's democratic intent to complete a job which has eluded the series of Labour Governments since the 1920s."
All three will also recognise the threat left unspoken - the contrary symbolic message if Labour again fails to reform the Lords after committing itself so far already. Tony Blair won't welcome the parallel, but the Lords are arguably as much a test of Labour as Hilary Clinton's health reforms were a test of the US president.