Distinctly English rather than distinctly British. As Lord Cooper said in MacCormick v. Lord Advocate, "the principle of the unlimited sovereignty of Parliament is a distinctively English principle which has no counterpart in Scottish Constitutional Law".
> no sitting parliament could ever restrict a majority of a future parliament from passing any law they saw fit
If the British Parliament tried to amend the Acts of Union 1707 to remove the protections granted to Scotland – for example, if it sought to abolish Scots law and replace it with English law – it is quite possible that the Scottish courts would rule such an Act of Parliament unconstitutional under Scots law, and also quite possible that the Supreme Court of the UK would uphold their ruling.
The idea of a First Amendment such as we have in America would be entirely foreign in Britain, for instance, since no sitting parliament could ever restrict a majority of a future parliament from passing any law they saw fit. Even Royal Assent at the time was largely ceremonial and usually carried out by Royal Commissioners rather than the monarch. In fact, the last time assent was withheld was 1708 under Queen Anne.