What the parent commenter meant, I believe, is that the UK Supreme Court is a new construct. Previously, the court of last resort (for cases like this at least) was the House of Lords, specifically those members known as the "law lords" or as their reply indicates, more formally the Lords of Appeal in Ordinary.

All current Supreme Court justices were drawn from the Law Lords and as a consequence of being Lords cannot vote for MPs. However, so far as I am aware, there's no requirement for a Supreme Court justice to be a Lord and thus no guarantee that any future Supreme court justice will be unable to vote for MPs.

What we may be witnessing, however, is more unspoken convention being established (that Supreme Court justices are made peers on appointment or shortly thereafter).

All that said, the UK Civil Service has a policy of neutrality. Civil servants are divided into junior and senior, depending on the role (not on age or length of service). Junior civil servants are discouraged from political commentary and being "card-carrying" party members and in particular holding any office in a political party. Senior civil servants are outright forbidden to be officers of political parties and any kind of public expression of views is also strictly forbidden.

This is because unlike the US, where the administration changes with the incoming party, the civil service remains unchanged and simply serves the incoming government.

The Judiciary in the UK are not technically civil servants, they're subject to similar restrictions. You can find the evidence of that here: https://www.judiciary.uk/wp-content/uploads/2018/03/Guide-to..., specifically: "There is a statutory prohibition on salaried judges undertaking any kind of political activity or
having ties with a political party". This extends to public demonstrations of any kind, and further extends to spouses of judges and close relatives as well.

So, even if a future Supreme Court Justice is not a lord, having any kind of political view that is publicly known is unlikely to be compatible with their appointment. This extends to judges. Unless the judge is a lord (and so restricted from appointing to the commons) they are allowed their own private views, and of course may vote (the same is true of the civil service) - but their public conduct is held to a standard of impartiality.

For further information, see this article https://www.theguardian.com/law/2012/mar/28/select-committee... on rejecting confirmation hearings by parliament and Lady Hale's speech on standing down as the head of the Supreme Court after the brexit/impartiality mess: https://www.theguardian.com/law/2019/dec/18/lady-hale-warns-... . Lady Hale also did a fantastic interview on the BBC regarding the functioning of the Supreme Court, and it's really worth listening to: https://www.bbc.co.uk/programmes/p07nkz4j

>> a disapproving Government could just tell Liz not to give them a peerage and they wouldn't get one

> I think they can only advise the Crown, not tell her what to do.

I should address this while I'm here. The Queen always acts on advice from ministers, even when that advice was illegal (see brexit) and even if she suspects it to be so. This is because the Queen strictly does not interfere with politics, ever (in private, she may however call the Prime Minister an utter moron, to his or her face, repeatedly for the duration of their weekly meeting, if she so chose. It's also legally required for ministers to inform her of what is going on in government, hence the despatch boxes).

As above, I'm not sure the requirement for being a Lord will necessarily hold for the Supreme Court. It does not appear to be in the legislation. The process is detailed on wikipedia: https://en.wikipedia.org/wiki/Justice_of_the_Supreme_Court_o... and involves the Judiciary selecting a candidate and passing that name to the prime minister, who is legally required to pass that name on to the Queen.

The most the political part of this process can do is ask for reconsideration. The judiciary may then submit a different name, or submit the same name again. In the event they do the latter it must be accepted. In the event they do the former, the Lord Chancellor may still chose the first name.

In summary: in the UK system, judges are far more independent of politics than in the US system.