As Britain’s David Cameron installed his second cabinet on Monday, he was urged by centrists not to interpret last week’s election victory as a mandate for radical change.

It is the prime minister’s unenviable task to keep his tribe happy but prevent it from behaving like a restorationist sect, writes Matthew d’Ancona in The Guardian newspaper. With only a razor-thin majority in Parliament, Cameron can’t afford to upset his more reactionary backbenchers, nor can he allow his party to lurch to the right or it will alienate voters in the next election.

The issue most likely to stir a rebellion is Europe, as it did for John Mayor, the last Conservative prime minister before Cameron came to power in 2010. He similarly commanded a small majority and party infighting contributed to a devastating defeat in 1997 when the Conservatives lost half their seats.

Cameron has already given Euroskeptics an in-out referendum on Britain’s European Union membership. But d’Ancona warns that the Tory right may not “take yes for an answer.” They could push Cameron to demand unreasonable concessions from other European countries, such as restrictions on the free movement of labor or a deep cut in Britain’s contribution to the union’s budget. If the prime minister gives in to such pressure, he would set himself up for failure in Brussels and raise the chance that British voters decide to opt out altogether.

Conservative Party leaders recognize the danger of overreach, writes the Financial Times‘s Janan Ganesh. “They know well enough that Britain has not become Texas overnight.”

At the same time, voters have given Cameron a mandate to eliminate the deficit by cutting back on state services, including welfare, and thrown the opposition into disarray. Labour will spend the next several months obsessing about its own future; the Liberal Democrats are almost wiped out and the Scottish National Party, now the third largest in the House of Commons, does not represent anti-austerity voters in England and Wales. This all gives the Conservatives leeway to pursue a radical agenda.

The laws on planning and land use can be loosened up, if rural Tories are pacified. Free schools and academies will proliferate. Power will flow to cities — George Osborne, chancellor of the exchequer, is a convert to a cause that Greg Clark, the new local government secretary, has proselytized for a decade.

The question is if the public will bear it. Britain is not “asking to be turned upside down by zealots,” according to Ganesh. d’Ancona adds, “The Tories would be quite wrong to interpret the election result as a green light to cut welfare as they please.”

The British deplore benefit fraud but they also deplore the politics of heartlessness in which efficiency trumps decency.

Cameron may agree and want to stay the course. But as d’Ancona points out, he no longer has Liberal Democrat coalition partners for cover. He can no longer claim the Conservatives have no choice but to pursue a centrist agenda. He now needs to convince them that’s the right choice to make.

Some rightwingers are irreconcilable to Cameron’s modernizing project. If they can’t be convinced, perhaps they can be bought off. Without a coalition party, Cameron has more jobs to hand out. The elevation of Thatcherites Sajid Javid and John Whittingdale to the cabinet on Monday and Cameron’s meeting with the chair of the backbench 1922 Committee, Graham Brady, suggest the prime minister knows there’s a tricky balancing act ahead.