https://en.wikipedia.org/wiki/Judicial_Appointments_Commissi...
(The JAC handles judicial appointments for England and Wales. There are JAC equivalents for Scotland and Northern Ireland. When there's a Supreme Court vacancy, a process starts up where members of the three JACs appoint people to a committee to recommend new SC justices.)
There are Supreme Court justices in the UK who have discernible political views (the retired Lady Hale was left of the average, and the retired Lord Sumption is more to the right) but their political affiliation has a comparatively small role in deciding whether they get a senior judicial appointment.
Nobody talks about justices having been appointed by a particular prime minister, for instance, because it is irrelevant. Nor does their political affiliation give you much of a clue how they are going to decide cases. This is also because in most cases, the Supreme Court sits as panels—unlike in the US, most cases are decided by a panel of five of the twelve judges, usually picked based on subject matter expertise (those with, say, family law experience will get picked for family cases, while those with more commercial experience are likely to be picked for commercial or financial disputes).
