Accepted wisdom is often that today’s MPs are historically loyal and servile, too cowed by the whips to vote independently or defy their party leadership. The reality is that the opposite is true – the work of Philip Cowley over the last decade or so has shown that the last Labour government broke records for the sheer level of dissent and backbench rebellion.

Now they are in opposition, Labour rebellions suddenly matter a lot less. They no longer have legislation to get through and it doesn’t actually matter a great deal whether or not their MPs turn up to vote. If faced with a contentious issue, they can allow a free vote and, as the Conservative-LibDem coalition has a majority of around 80, there are unlikely to be many close votes. Only on the most contentious issues will the media even notice if Labour’s MPs rebel. During their long years in opposition, the only time that the media paid attention to rebellious Conservative MPs were in the vote over the war in Iraq, and the whipped vote upon gay adoption when it became a symbolic battle between modernisers in the party and the waning authority of Iain Duncan Smith.

Over the last 13 years, the Campaign Group has provided Labour’s usual suspects, with Jeremy Corbyn, John McDonnell and Alan Simpson regularly the most rebellious Labour MPs. However, the Campaign Group lost a large number of members as a result of the 2010 election: Alan Simpson, Lynne Jones, Bob Marshall-Andrews and Ann Cryer were among 10 retirees, while David Drew was defeated and Clare Short and Bob Wareing had already left the party.

This leaves Labour’s awkward squad with depleted numbers. The most obvious new recruits among Labour’s incoming MPs are John Cryer, the former MP for Hornchurch now returned in Leyton and Wanstead, and Ian Lavery, Arthur Scargill’s successor as president of the National Union of Mineworkers and now the MP for Wansbeck.

Of course, this all assumes that Labour continues in the New Labour mould. If instead they end up tacking to the left to try and create ‘clear red water’, it may be the other fringe of the party that provides dissent – and there the likely suspects are less predictable. Many of the core Blairites have now departed parliament and more interesting could be the future of those MPs once loyal to Gordon Brown.

The Maastricht rebellion aside, Conservative MPs tend to be far less rebellious than Labour MPs, either in or out of office. Back in 1996, Cowley observed that: ‘Labour MPs dissent more often than Conservatives; they dissent in great numbers than Conservatives; and they dissent on more issues than Conservatives.’ He was proved entirely correct by the subsequent Labour government.

However, the Conservative-Liberal Democrat coalition has a huge ideological span: there can be comparatively little that unites Simon Hughes or Steve Webb with Edward Leigh or Andrew Rosindell. It seems likely that David Cameron’s problems will come from the right of the party and the Cornerstone group – in fact, the fear among some there seems to be that the LibDem coalition will allow Cameron to ignore his right flank in much the same way as Tony Blair and Brown ignored the Campaign Group.

There are also some potential thorns in Cameron’s side from those who should in theory be his natural allies. The need to sustain his coalition with the LibDems will likely prevent Cameron drifting rightwards on the environment or civil liberties, but he also has MPs of his own who may object to any backsliding. Zac Goldsmith is clearly a moderniser in the Cameron mould, but his promise to resign and force a byelection should there be any hospital cuts in his constituency indicates he may not be easily whipped. Former shadow home secretary David Davis would probably be as rebellious over any civil liberties infringements as his new Liberal Democrat colleagues.

Over half the parliamentary Conservative party are newcomers and might be expected to follow the whips’ orders for the time being. However, the 2005 intake of Conservative MPs contained many rebellious spirits – people like Philip Davies, Philip Hollobone and Peter Bone rapidly became and – unless they become part of the government – are likely to remain conspicuous rebels.

The huge new intake of Conservative MPs are likely to contain some more in that mould, though Cameron does at least now have the advantage of being able to offer patronage and ministerial office. Some of the loyally Thatcherite elements of the new intake may have their eyes on future ministerial office rather than a career as a backbench rebel. For now, ambition will keep many in line. Once the ranks of ex-ministers and ‘never will be ministers’ start to grow, things will get more difficult.