In the event Mr Beackon's fellow party members failed to gain election and he lost his seat. At the same time Liberal Democrat control of the council was swept away by Labour. Since then things have been quiet. So have peace and a return to traditional politics broken out in the East End?
When the Labour Party regained control after eight years of decentralising Liberal Democrat rule, it immediately set about restoring central control in the borough. By the end of the year Labour hopes to have completed the destruction of a unique system of neighbourhood self-government which had been praised by many experts. A recent academic study, for instance, described it approvingly as involving "an unprecedented degree of political devolution".
Local Liberal Democrats are predictably bitter at what they see as a return to an unpopular, old-fashioned, autocratic, highly centralised approach that has long been out of fashion in the rest of Labour-controlled inner London. The Liberal Democrats saythat residents are deeply unhappy and claim that council workers fear for their jobs and the quality of service they will be able to provide.
Now, six months into Labour's counter-revolution, the resignation of a Labour councillor has given the Liberal Democrats an unexpected chance to test the supposed popular dissatisfaction with the new regime. Next week voters in Lansbury ward, Poplar, will be asked to choose from Labour's Michael Keating; Mr Beackon, who is attempting a comeback; and Peter Hughes, the former Liberal Democrat leader and prime architect of the devolution policy.
If public discontent cannot be measured, political rancour is still palpable. The atmosphere at the town hall is strained. "If you open your mouth in council you are screamed and shouted at," says Janet Ludlow, leader of the seven-strong Liberal Democratgroup. "Labour's management style is: `Sod you. We do what we like.' They are deliberately trying to freeze us out. We are given no power, even in the wards we did win."
Such exchanges can be dismissed as political knockabout. But it is worth considering what was unique about the Liberal Democrat experiment in decentralisation. How did it work on the ground? And what, finally, went wrong?
The Liberals' aim in 1986 was admirable: to enable local people - represented by councillors controlling annual budgets of up to £30m - to decide the sort of housing, education and social services they wanted in their immediate neighbourhoods. They wouldensure that local priorities were met rapidly and efficiently.
Councillors for each locality were to have command of administrators and manual workers in seven self-governing neighbourhood centres, dubbed mini-town halls. These buildings, instantly accessible to the public, were built across the borough at a cost of£10m.
Labour says too much power came to reside in handfuls of councillors - between five and seven who controlled each neighbourhood centre. Within the law they could, and did, hire and fire staff and allocate council accommodation as they saw fit. The possibilities for patronage or exploitation of local grievances were "immense", says John Biggs, the Labour leader of the council.
So what did decentralisation mean? In Bow, for example, council policy for the neighbourhood under the Liberal Democrats was decided by seven councillors based near the Roman Road. All Liberal Democrats, they controlled 600 staff and had an annual budgetof almost £30m.
The Bow neighbourhood centre is still operating, although its autonomous budget has been clawed back under central Tower Hamlets control. When I visited the centre recently it was apparent that the key to the working of the scheme is the "One Stop Shop" on the ground floor of the neighbourhood centre. This is an advice and action unit to which locals can bring any problem for on-the-spot resolution. No resident of Bow need go anywhere else to sort out a problem with the council, because all officials serving the neighbourhood are housed in the centre.
The five staff deal with up to 600 queries a day. On a bright winter morning, Nellie Molloy had come in to voice her objections to a council car park scheduled to be built alongside an old people's home on her estate. The planning officer was summoned toone of 12 interview rooms to discuss her worries.
A young couple popped in to resolve a dispute about their rent. The rent officer sorted things out. John Woolhouse turned up to show staff a letter from the local Labour MP protesting at the closure of the centre. "I was devastated when I heard they wereto shut it," Mr Woolhouse said. "This little shop is a haven from heaven."
Morale among the staff at Bow is low. "I don't think we will be able to offer as good a service in future," said one official, who declined to be named. "The One Stop Shop will probably stay. But in future when people come in with, say, a housing or environmental health problem, we won't be able to sort things out on the spot. All we will be able to do is phone the central directorate responsible and try to fix them an appointment."
By common consent, Bow neighbourhood centre was one of the most successful mini-town halls. But, for a while, most neighbourhood control appeared to work well. Tower Hamlets earned plaudits from experts as service delivery improved dramatically in the late Eighties. Streets were cleaned more efficiently and council housing repaired promptly. Polls conducted for the council by Mori showed an unusually high level of satisfaction among residents. A high and steadily rising proportion of the population voted in local elections. So is it mere vindictiveness and an unhealthy desire for central control which have driven Labour's determination to recentralise?
Mr Biggs says not. Under the Liberal Democrat regime, he suggests, tiny cliques of councillors in some mini-town halls became too powerful, parochial and inclined to play on intolerence of "outsiders"
- particularly members of ethnic minorities. He says that in recent years the borough has absorbed thousands of Bengali immigrants and Somali refugees, which has strained already inadequate housing, social services and schools. The crisis came to a head on the Isle of Dogs, a neighbourhood with severe housing problems, when Mr Beackon was elected as a councillor in the autumn of 1993.
Paradoxically, the neighbourhood council there was controlled by Labour throughout the years of Liberal Democrat rule. Mr Beackon's success, by only seven votes, was widely seen as a reaction against the housing policy of the five Labour councillors. Some older inhabitants apparently thought "their" Labour councillors were too sympathetic to Bangladeshis seeking council accommodation.
With the election of Mr Beackon the dangers inherent in Tower Hamlets' extreme form of decentralisation were suddenly exposed. If two more BNP candidates had been elected in May, these extremists would have been in a majority among the councillors running the Isle of Dogs neighbourhood centre, which they pledged to rename Oswald Mosley House after the British fascist leader.
According to Labour supporters, the Liberal Democrats bore a further responsibility for the Isle of Dogs debacle. They had allegedly let the racist genie out of the bottle by playing on chauvinist attitudes among locals anxious to keep scarce council accommodation for their (white) sons and daughters. Late last year the Liberal Democrats nationally appeared to confirm this view when they censured the local party for condoning or exploiting racist attitudes.
Before the May elections Labour poured activists into the borough to "fight fascism". The Liberal Democrats, however, held back. Tower Hamlets council had become an embarrassment. "The national party stabbed us in the back," Ms Ludlow says. "Nobody came down to help us."
Whatever the reason, the turnout was high for a local election, and Labour benefited. Mr Beackon lost his seat to Labour, along with dozens of Liberal Democrat councillors. The borough is firmly back in Labour hands.
Many in the Labour group are determined to put an end to what they see as an ill-conceived exercise in community politics which played into the hands of local bigots and racists. But others simply resent their party's eight years in the wilderness, and the destruction of a highly centralised political machine that had served them well for more than half a century.
It is still unclear whether Labour will be prepared to jettison a Liberal Democrat experiment that at its worst gave power and patronage to tiny cliques of local councillors, while retaining the system of accountable, local service delivery that proved efficient and popular. As the conflict intensifies, the British National Party hovers in the wings, ready to exploit the deep gulf between the two parties.