Unsurprisingly the early days of Labour’s leadership contest are defined largely by where candidates stand in relation to the party’s great election winner. Is X following the course set by Tony Blair? Is Y moving away? The questions are bound to erupt after confidence-sapping election defeats. While the future is hazy, there is a past in which the party used to win.

But rather than dwelling on Labour’s complex, still highly charged recent history, the candidates to succeed Ed Miliband do have another leader to learn from, one who has also won elections. He is there in front of their eyes and set out on his course in a very similar context to the one facing the potential Labour leaders. He is none other than the newly elected prime minister.

I do not mean they should adopt the policies of David Cameron, but there are lessons to be learned from his leadership, ones that are rarely explored. Indeed I was struck by how little focus there has been on Cameron as a leader when watching a lecture from the constitutional historian, Vernon Bogdanor, on the 2015 election. Of his many thought-provoking observations, Bogdanor notes that Cameron is too easily underestimated. The Tory leader has “seen off” Brown, Miliband, Clegg and Cable while being the first modern serving prime minister to increase his party’s share of the vote.

We should not get overexcited, and Bogdanor does not. It is equally easy to overestimate Cameron, or rather the strength of Cameron’s position. Cameron’s senior advisers do not do so. While relishing the unexpected opening-up of political space, they know there is unavoidable trouble ahead over Europe, wonder whether they will have majorities for key legislative items and what will happen to their proposals in the Lords.

But look back to what Cameron inherited in 2005 when he became the party’s leader. There was still quite a lot of talk about whether the Conservatives could ever win again, hyperbolic speculation now directed towards Labour. Compare such talk when Cameron became leader with the Queen’s speech delivered last week, one crammed with radical proposals rooted firmly on the right and projected as “one nation” Toryism.

Like Cameron in 2005, the next Labour leader will face a prime minister who will not fight the general election, and with an electoral mountain to climb. For Labour the parallels are much closer than they are to Blair’s early days. When he became leader in 1994 the Conservatives were in disarray and Blair knew he would be facing an already weakened John Major at the general election.

Here are some of the underexplored strengths of Cameron’s leadership. At the beginning he deployed a brilliant phrase to suggest change while remaining ideologically in tune with a party on the right. He declared that “there is such a thing as society, but it is not the same as the state”. What appeared to be a rebuke to Margaret Thatcher was in fact a more human way of making the same arguments she had made. Language is extremely important in politics, a weapon. The recalibration of a familiar argument gave Cameron an audience in places that extended beyond his party. Miliband’s talk of “predistribution”, “predatory capitalism” or a “better plan” was not an equivalent weapon.

While Cameron looked outward well beyond his party, noting a potential ally in Nick Clegg well before the hung parliament in 2010, he ensured some of his leading Tory radicals were pulling the policy levers. The levers were aimed at what one of the pullers described to me as “reheated Thatcherism”. But Cameron would never put it like that in his engaging, emollient public performances.

The levers were aimed at ‘reheated Thatcherism'. But Cameron would never put it like that

His radical lever-pullers are often hidden from view. Oliver Letwin is never allowed to give interviews, but is more influential than ever now. When Michael Gove was causing trouble he was moved fleetingly behind the scenes until the election was safely won and is now back with another big reforming role, at the Department of Justice. This is bolder leadership compared with the new Labour era, where “reform” was narrowly and timidly defined.

During Cameron’s leadership the Conservatives have become more alive as a party, impressively animated by ideas and debate. Cameron appears to be an orthodox Tory but likes having daring thinkers around him, even if they do not last that long.

Steve Hilton, who must have given more interviews in the last fortnight than Vernon Bogdanor would have done if there had been a hung parliament, is one example. Hilton is promoting his book fizzing with ideas. In recent years Conservative party conferences have been far livelier than Labour ones, which have been deadened by fearful control freakery. The next Labour leader must not be frightened by internal debate. That does not mean returning to the 1980s, but the other extreme of dead unity over “on message” banalities is just as fatal.

Equally important is what Cameron didn’t do. In his early years he did not spend his whole time apologising for his government’s handling of the exchange rate mechanism crisis, when he worked for the then chancellor, Norman Lamont. Nor, incidentally, was Margaret Thatcher asked to apologise for the three-day week when she stood for the leadership of the Conservative party in 1975, even though she had been a cabinet minister when the lights went out around the UK.

The ongoing media focus on whether Labour candidates should “apologise” for their government being responsible for the global economic crash in 2008 is a trap. If Cameron or Thatcher had received similar media treatment, they would not have gone around pathetically saying sorry but found other policies and language to show how they intended to move on.

Assuming the next Labour leader survives for five years, he or she will be facing a different Tory prime minister at the next general election. In the meantime they should take a few notes on how the current occupant of No 10 led an apparently doomed party to power while largely sticking to its ideological course.

• Steve Richards presents rock’n’roll politics at King’s Place in London on Monday 15 June at 7pm