Sometimes in a coalition, it suits both parties to have a row. At others, one partner will be much happier to have a public spat than the other.

The dispute between the Conservatives and Liberal Democrats over immigration falls into the second category. Nick Clegg, Vince Cable and other Liberal Democrats have attacked  the Home Office campaign in which ad vans toured some London boroughs urging illegal immigrants to “go home or face arrest”. Council leaders say it has caused offence and harmed community relations.

Privately, senior Conservatives are happy to have a row about immigration with anybody, as long as they are on the “tough” side of the argument. “Clegg walked right into the trap,” claimed one Tory MP. Even the UK Independence Party attacked the campaign as “nasty”. Nigel Farage, its leader, said: “What the billboards should say is, ‘Please don’t vote Ukip, we’re doing something’”.

Labour was more cautious than the Liberal Democrats about criticising the campaign. It knows the public have doubts about its record on immigration and does not want to be seen as “soft” on the issue.

Today Grant Shapps, the Tory chairman, claimed immigration would rise under a Miliband government. It is no surprise the Tories are playing the immigration card now that Lynton Crosby, the Australian political consultant, is their election strategist.  When he ran the Tories’ 2005 campaign, the country was plastered with posters asking: “Are you thinking what we’re thinking?”, with immigration one of the themes.

Mr Clegg was brave enough to disown the ads. The Deputy PM sees the campaign as another sign the Tories have vacated what he calls the “decent centre ground” of British politics.

Like Mr Shapps, Mr Clegg gave us a preview of the 2015 election, talking up the choice between David Cameron and Ed Miliband. In contrast, the Liberal Democrats are keener to show that “coalition works”. At his monthly press conference, Mr Clegg unveiled a booklet listing the party’s achievements in government.  While the rise in tax thresholds to £10,000  next year bears a Liberal Democrat stamp, he also claimed ownership of measures such as a council tax freezes and lower than expected fuel duty, saying these “wouldn’t have happened without the Liberal Democrats”. The Tories will dispute that.

The Liberal Democrats’ manifesto will set out their non-negotiable “red lines” in any coalition negotiations if no party wins an overall majority in 2015. Today Mr Clegg urged the Tories and Labour to follow suit. He will be disappointed. Although another hung parliament is a real possibility as Labour’s opinion-poll lead shrinks, the two biggest parties think the rules of the game mean they can only talk about winning.

Mr Clegg believes his party has reached a fork in the road: it must choose between being a party of government with a chance to implement at least some of its agenda, and the comfortable impotence of opposition. The conference in Glasgow next month will provide some important clues about which direction it will take. Unlike the Tories’ and Labour’s annual gathering, it decides party policy. Liberal Democrat members will decide whether to propose a return to a 50p top tax rate; whether to scale down the Trident nuclear weapons system and whether to keep £9,000 university tuition fees. Some activists fear Mr Clegg wants to turn the Liberal Democrats into a “Tory-lite” party.

In public, the Tories and Labour will dismiss the Liberal Democrats. In private, Mr Cameron and Mr Miliband will take a keen interest in Liberal Democrat policy decisions, because they know they may be picking up the phone to Mr Clegg on 8 May 2015.