I won't pretend to be a political scholar so I'll just quote the first couple of results that came up:
The abstract of Peret's 2021 study "A divided kingdom? Variation in polarization, sorting, and dimensional alignment among the British public, 1986–2018" says:
Understanding changes in the structure of public opinion is necessary to evaluate both contemporary claims about political divisions in Brexit Britain, as well as to uncover any long‐term mapping of public opinion on the depolarization and subsequent polarization of elites from the birth of New Labour to the aftermath of the Great Recession. I assess trends from British Social Attitudes surveys, utilizing recent conceptual and methodological distinctions between different features of public opinion change. I find that the public, on average, moved to the left during the early 1990s, to the right during New Labour, and back to the left from 2010. Such oscillations are even more pronounced for positions along a welfare dimension. In contrast, average positions along a libertarian‐authoritarian dimension were constant until around 2010, when the public became more liberal. Polarization of left‐right opinion has increased in recent years but does not match that estimated between the mid‐1980s and early 1990s, while low and stable levels of polarization are estimated along libertarian‐authoritarian and welfare dimensions. Overall trends are dis‐aggregated by social class, educational attainment, party identification, strength of partisanship, interest in politics, and position on Europe. Further, the relationships between positions along these three ideological dimensions vary systematically across time and between groups.
This indicates that whilst on the small scale we've had recent polarisation it isn't a new phenomena, having seen more extreme polarisation in the mid-1980s-early 1990s.
The title question:"the UK has become more polarised in recent years?" is supported by this. However the text of your question hypothesises that "the UK is in one of its most politically polarised times" - which is not supported by this research. The UK has been hugely polarised in the mid 80s-early 90s, more so than it is today.
The Conclusion from Grechyna, D. Political polarization in the UK: measures and socioeconomic correlates looking at a period 1991-2007 says:
This paper analyzed regional political polarization in the UK. Three common measures of polarization were computed from the individual responses to political statements in the British Households Panel Survey. Given that the political statements considered are not directly comparable, I used confirmatory factor analysis to estimate unobserved political polarization underlying the individual responses to different statements. Different measures convey similar patterns of regional polarization and suggest that political polarization in the UK decreased during the period covered by the survey, 1991–2007.
Further supporting the heightened polarisation in the early 1990s decreasing over time up to 2007 (just before the 2008 financial crisis).