But May's speech at the World Economic Forum today shows that she is not the new Thatcher.
She's the new Tony Blair.
Her speech was an explicit bid for the centre ground. She - somewhat surprisingly - rejected some longheld Tory orthodoxies. And, as she has done before, adopted some of Labour's old policies.
Listen to this:
"Across Europe parties of the far left and the far right are seeking to exploit this opportunity - gathering support by feeding off an underlying and keenly felt sense among some people - often those on modest to low incomes living in relatively rich countries around the West - that these forces are not working for them."
"And those parties - who embrace the
This morning, I want to set out a manifesto for change that responds to these concerns and shows that the politics of the mainstream can deliver the change people need."
Thatcher could never have said that. Tony Blair could have, easily.
May believes the centre has been evacuated by Labour's turn to the left under Jeremy Corbyn. By standing firmly in the middle she also places a boot on the throat of the Liberal Democrats, who were annihilated at the 2015 general election. With both Labour and the the Lib Dems out of the way, May clearly feels she owns the battlefield.
That strategy is working. Look at this poll from YouGov:
Labour in opposition ought to be streets ahead of an incumbent government at this stage. Yet it remains far below even the level it achieved when it lost the 2015 vote. Here is long-term trend:
Whatever you think of Corbyn's return to socialist principles, it is now time to admit that Labour is a dying force in British politics. As my Business Insider colleague Adam Payne wrote: "Research by academic Matt Goodwin and others suggests that Labour must lead the Tories by at least 12% in order to form a majority at the next election. On this basis, Corbyn's Labour is 29% points behind where it needs to be."With that context, here is May talking about the less well off - people who ought to be Labour voters:
"Talk of greater globalisation can make people fearful. For many, it means their jobs being outsourced and wages undercut. It means having to sit back as they watch their communities change around them."
"And in their minds, it means watching as those who prosper seem to play by a different set of rules, while for many life remains a struggle as they get by, but don't necessarily get on."
"... at the same time as promoting this openness, we must heed the underlying feeling that there are some companies, particularly those with a global reach, who are playing by a different set of rules to ordinary, working people."
"... That means several things."
"It means businesses paying their fair share of tax, recognising their obligations and duties to their employees and supply chains, and trading in the right way."
All of that could have been included in a Corbyn speech.
Or a Blair speech.
It's not just that she is stealing from the Labour playbook. She is also tossing out - or at least she says she is - key planks of bedrock Conservative belief, in particular the idea that free markets fix everything and the government's main job is to get out of the way. Here's May speaking in Davos again:
"For government, it means not just stepping back and - as the prevailing orthodoxy in many countries has argued for so many years - not just getting out of the way. Not just leaving businesses to get on with the job and assuming that problems will just fix themselves."
"... And for business, it means doing even more to spread those benefits to more people. It means playing by the same rules as everyone else when it comes to tax and behaviour, because in the
"... Because if you are someone who is just managing - just getting by - you don't need a government that will get out of the way. You need an active government that will step up and champion the things that matter to you."
There was a time when it would be heresy for a Conservative leader to say that government ought to be a more active champion of the poor, or that big corporations ought to pay tax like everyone else.
Of course, these are just words, and May doesn't always stick by them. After she was elected, she proposed a new law adding workers' representatives to the boards of large companies. That was a fantastically promising, essentially left-wing, idea that would inject new blood and fresh perspective into the upper management of Britain's biggest firms. But she walked away from it weeks later.
Blair remains hated by Labour voters because of his fatal error on the second Iraq war. But May appears to be focused a bit more on the rest of his historical record: It was only under Blair the centrist that Labour was able to return to government, winning four straight general elections.
May no doubt has that in mind as she looks to the 2020 election - one year after Article 50 expires, and with a country potentially falling into recession as its largest and closest trading partner levies taxes and barriers on UK goods.
She's going to need all the votes she can get. And it looks like she is happy to take them from Labour and the Lib Dems.
This is an opinion column. The thoughts expressed are those of the author.