There are no particular crimes or offenses that "asks for the British government to strip his/her British citizenship". The only provision which allows the British government to involuntarily strip someone's British citizenship that was properly obtained is section 40 subsection (2) of the British Nationality Act 1981, which allows the Secretary of State to strip someone's British nationality if he/she "is satisfied that deprivation is conducive to the public good". Under subsection (4), this stripping is only allowed if it would not make the person stateless (except for British citizens by naturalization, which can be stripped under subsection (4A) under certain conditions if the Secretary of State "has reasonable grounds for believing" that the person is able to acquire another nationality).
(Note that I said "citizenship that was properly obtained", because if the citizenship was obtained through fraud or misrepresentation, it can be stripped under subsections (3) or (6) even if it will make the person stateless. But, arguably, that isn't so much a "stripping" of citizenship, as a determination that the person was never properly a citizen in the first place.)