None of the governments of the UK in the past century have been either far right or far left. There has been some movement around a middle, by the various major parties. I don't think you can look just at the governments because in the end the political agenda and public discourse comes out of the different factions and viewpoints in the larger population.
So sometimes we can see two major approaches at the same time, often in tension with each other. (Which is not necessarily a bad thing at all.) And I would also say that there can be a difference which is dominant in which sector of life.
In terms of economics there has been a real narrowing of possibilities for parties, and indeed nations. Under a globalist economy, there are really only a few options. A lot can't really be controlled by any state, at most they can choose to opt into the global economic structures, or not. There can be advantages and disadvantages, but they aren't hugely different in the end, barring complete isolationism.
Within the nation there is more room for divergent approaches in terms of things like privatization, social programs, centralization vs distribution of power, collectivism vs communitarianism vs individualism, and so on.
Overall I think the British have a small-c conservative approach to governance, the whole structure of governance is built on that and it's been remarkably effective and stable and flexible, which is an unusual and good combination. I deliberation don't say "right wing" here because I think in fact that certain kinds of leftism are actually quite conservative in their approaches, emphasizing low level, grass roots community structures and institutions that act to enhance fairness and justice in society.
Or to put it another way, I think much of British leftism and conservatism are both inclined to a very communitarian impulse, which is not the same as the kind of socialist collectivism that you sometimes see on the left and which has dominated in some places, and it's not the same as the kind of right wing libertariansm that we tend to see come out of the US.
That right wing libertariansm and high level socialism both tend to morph into a kind of oligarchic control by elites combined with a high level of bureaucratic "expert" governance. Left wing elitism and id politics also fits in here. Neither are really liberal-democratic. The latter tends to be the servant of the former, often unwittingly, IMO.
Identity politics is its own thing in a way, but it has strong features of a kind of collective determisnism that is what Sowell calls "unconstrained".