"Why do refugees come to the UK?"

Rather than go into the historic, cultural or familial reasons, the actual answer is that to a first approximation, they don't. The UK towards the bottom of European nations on a per capita basis in terms of refugees and asylum seekers hosted.

Of around 6mn displaced Ukrainians, there are about 200k in the UK
Of c10mn displaced Afghans, maybe 30k here.
Of 13mn displaced Syrians, maybe 30kish here.

The "problem" isn't "UK pull factors". It's lack of UK care.