British citizens currently in Israel or the Occupied Palestinian Territories are now encourage to register here:

https://www.register.service.csd.fcd...an-territories

This is regardless of whether you wish to leave at the moment, though I understand work is underway to provide a safe corridor. You need to have a UK passport to register, however it can be an expired one - so long as it has 9 characters.

The FCDO advice for Israel, Jerusalem and Palestine is here
https://www.gov.uk/foreign-travel-advice/israel