Andrew Grice: The coalition leaders may have bonded, but have their parties?

The new government has achieved a lot in just two weeks. It would surely have taken about two months on the Continent, where coalitions are much more common.

The Conservatives and Liberal Democrats have reached agreement on £6.2bn of immediate cuts, a significant U-turn by the Liberal Democrats since the election campaign which they struggle to explain in interviews. In return, Nick Clegg has persuaded David Cameron to adopt a long list of political reforms including a House of Lords elected by proportional representation and a referendum on the voting system for the Commons.

The coalition partners have reached a deal on about 400 policy areas, even if more than 20 tricky issues remain under review. Their long "coalition agreement", published last Thursday, meant there were few surprises in the Queen's Speech yesterday.

Despite the obvious need to compromise, the Government seems to have achieved the momentum Mr Cameron would have wanted if the Tories had won the election outright. Yesterday he reminded some Tory MPs of Margaret Thatcher with a forceful and no-nonsense display in his first major Commons speech as Prime Minister. "He is really motoring – determined, robust and resolute," said one aide.

His bonding with Mr Clegg is real, not for show. The two leaders find themselves instinctively reacting the same way when problems arise. They are very similar political animals. Their challenge now is to make sure their two parties bond too. Although no one is rocking the boat, there are signs that the "new politics" the two leaders want to achieve has not yet spread to their MPs.

Peter Lilley, the former Cabinet minister, was cheered to the rafters by his fellow Tory backbenchers when he made a witty but pointed Commons speech. While supporting the coalition, he made very clear that it was strictly a temporary arrangement and that the Tories would want to win more seats next time. Warning about the dangers of coalitions, he said: "Should they become the norm rather than the exception, they should give parties an easy excuse for abandoning manifesto pledges and a temptation to make pledges they have little intention of keeping."

Simon Hughes, a Liberal Democrat backbencher on the left of the party, asked the Prime Minister a less-than-friendly question about house-building, but the significance was that Mr Hughes referred to "his" government – Mr Cameron's, that is. The PM replied that he hoped Mr Hughes would come to regard it as "our" government.

Team Cameron is keen to integrate the two party's media operations to reduce the prospect of damaging splits, but the Liberal Democrats want to reassure their members that they are keeping the flame burning. Yesterday they issued a 23-point list of "Liberal Democrat policies announced in the Queen's Speech", including the four priorities in their manifesto – fair taxes, a fair start for children, a green economy and a comprehensive clean-up of politics.

Mr Cameron has said he hopes the coalition will succeed by its success. In other words, that it will win over doubters in both parties and among the public, although the early evidence is that people rather like the idea of parties co-operating rather than scoring points off each other.

Sitting alongside each other on the government benches yesterday, Tory and Liberal Democrat MPs somehow did not look like comfortable bedfellows – unlike their two leaders on the front bench. A lot of hard pounding lies ahead if the coalition is to prove a success.