The UK constitutional system has been expanding its “checks and balances” quite a bit.
In the early 2000s the UK Supreme Court was granted a great deal of institutional autonomy. During the Brexit fiasco, it had no problem flexing its muscles.
The House of Lords had likewise been reformed and is much stronger and meritocratic (there’s still work to go on it).
Likewise subsidiary nations and municipalities have an increasingly large amount of independence. If Westminster passed surveillance laws unpopular in Scotland, they likely wouldn’t be implemented in Scotland.
The best example is probably Northern Ireland. There’s much greater support for surveillance powers in NI. But those expanded powers are combined with much greater accountability and oversight of security services.
Some parts of the British Home territory have too little surveillance. Both the City of London and Jersey have a reputation for laundering dirty money - something unthinkable in Northern Ireland.
Nothing about the UKs future is clear.
But I don’t think they need the EU to prevent them from passing overly broad or weak surveillance laws.