The best, and boldest, line in Theresa May's speech came towards the end – as it often does – in this repudiation of Margaret Thatcher's "there is no such thing as society": "We succeed or fail together," the prime minister said, evoking the spirit of the Brownlee triathlon brothers. "We achieve or fall short together. When one of us falters, our human instinct is to reach out our hand and help them over the line. There is more to life than individualism and self-interest."

The woman who delighted her MPs at her first PMQs with an uncannily accurate impression of the first female Prime Minister was making a clear break with one of the central tenets of Thatcherism. It was significant, because it showed how she does not see herself as a Margaret Mark II, as some on the Tory right would fantasise.

Yes, Thatcher appealed to working class voters and championed grammar schools in the same way May seeks to now. But Thatcher would not have staked a claim to the "centre ground" as May did in the Birmingham conference hall – she preferred "common ground", the phrase reincarnated by David Cameron in his speech last year. With Labour abandoning the centre ground, May wants to be the heir to Blair, to find a third way as a route to electoral success. But May's speech was not triangulation. It was a wobbly, shifting shape that defies geometry.

If May had stuck to the "reach out our hand" theme throughout, it would have been a fine debut leader's conference speech with broad electoral appeal. Instead, it was shot through with inconsistency. How can a Prime Minister talk of helping people over the line when her government talks such hot rhetoric on immigration, with plans to "shame" companies that employ foreign workers?

Despite rumours that Home Secretary Amber Rudd is softening her line on this policy, May nevertheless talked of a "social contract that says you train up local young people before you take on cheap labour from overseas" and how "life doesn't seem fair" to people who "find themselves out of work or on lower wages because of low-skilled immigration".

The "British jobs for British workers" trope was controversial when Gordon Brown used it in 2007. Post-Brexit, with anti-immigrant hate crime on the rise, it is deeply irresponsible to warn, as May did, that "resentments will grow" and "divisions will become entrenched". It is possible to acknowledge the low pay and lack of opportunities of "local young people" without playing one group off against another. If anything will entrench division, it is that.

All of this jarred with May's declaration that it does not matter where you are born but "the talent you have and how hard you are prepared to work". May said the UK is a country "built on the bonds of family, community, citizenship", but there is another strong tradition that is being ignored by this post-Brexit Tory rhetoric: that of the hardworking immigrants who have helped shape 21st century Britain. From bus drivers like the fathers of Sadiq Khan and Sajid Javid, to the doctors and nurses who keep our NHS alive, to the international academics who discovered graphene at Manchester University. And in a passage that emulated Ed Miliband rather than Thatcher or Blair, she railed against Sir Philip Green and the Big Six energy companies putting two thirds of customers on the most expensive tariffs.

The prime minister said she wanted the nation to be a "Global Britain" and promised to "not abandon our friends and allies abroad" nor "retreat from the world", yet it felt like the most isolationist speech delivered by a party leader in recent times.

Blairism was pro-immigration, pro-Europe and liberal. May is not the heir to Blair. May knows she has to fight off Ukip on her right flank – and with the resignation of Diane James and that party in disarray, she has a perfect opportunity to do that – as well as wade into Labour's vacated territory on the left. But the phrase "centre ground" is misleading, particularly post-Brexit.

It is easy – and justifiable – to want to speak for the 52 per cent who voted to leave the European Union. But it is just as easy to forget that the nation is divided almost down the middle. The 48 per cent lost the referendum and, in terms of May and her government, they have lost their voice too. What did the 48 per cent think, for example, when she repeated "a change has got to come"? What did EU national migrants, settled in this country, think when she said "this is a turning point for our country"?

In a sense, with Labour under Jeremy Corbyn as it is, none of this matters: the Conservatives will likely win the next election. But if May wants to appeal to the centre ground, she needs consistency, not contradiction; she needs to speak of unity, not stoke fear.

Jane Merrick is a freelance journalist and former political editor of The Independent on Sunday. She writes an allotment blog, Follow her on Twitter @janemerrick23