It's a good question - but the reality is, British politics only ever functions in the centre ground. Every lurch to the right or left is met with resistance from the centre ground. The populism of both Johnson and Corbyn has been roundly rejected (thank fuck). So yes, Labour centre and Tory Centre have more in common with the fringes of their own party, but I don't see that as a bad thing. I'd rather have Rory Stewart than Suella Braverman, and I'd rather have Starmer than Corbyn. I have faith that most people are inherently moderate and kind. Democracy is about consensus and that is moving slowly to the left.... see the history of LGBTQ+ inclusion since 1969. It might feel slow, but slow and steady is how it has to be.
The alternatives to the centre ground aren't nice places. The far right open concentrations camps, the far left opens gulags, the overall experience is the same for the people inside - and the British public will reject either extreme side regardless of whether they couch their policies in nationalism or identity.