The closest the UK has to a constitution-like protection is getting it to sign an international treaty, e.g. what's behind the Human Rights Act — after Brexit, some of the usual suspects have been campaigning to also leave the corresponding treaty, because it limits the sovreign right of each government to completely disregard what the previous one did.
To answer your question, the other solution is to do what I did in response to the Investigatory Powers Act 2016: leave the country.
> international treaties have no effect under UK law, unless Parliament decides to pass an Act containing its provisions
Indeed, all I claim is that leaving treaties comes with consequences that mean they stick, hard to change in practice even when it's theoretically just another law that only needs a parliamentary majority to delete.
Functional closest equivalent, not identical in every detail.
To answer your question, the other solution is to do what I did in response to the Investigatory Powers Act 2016: leave the country.