There is the European Convention on Human Rights, to which UK is a signatory and has now incorporated into British law. Unfortunately the ECHR is the product of a rather different age than the American constitution. The rights set out there are muscular indeed, but the qualifications in the subsequent paragraphs - inserted by cautious ruling elites, self-conscious of the need to repress dissent - often negate the rights entirely. Most contain caveats about national security, public morals and welfare, which loopholes are bigger than the rights themselves. A few people (including myself, but perhaps more plausibly Conor Gearty) have argued that the application of the ECHR creates a sum reduction of liberty.
The harassment/stalking laws have caught a lot of people unawares because they are framed in terms that those enlightened liberals amongst us are likely to sympathise with - such as the need to stop violence against women. (That said, Amnesty spokesman Conor Foley once pointed out once that the anti-stalking law had been used most often against hunt saboteurs!).
-- James Heartfield