Under the Regulation of Investigatory Powers Act 2000 Part III Section 49 the police can, with a certain procedure, require one to provide a key with threat of custodial sentence up to 2.5 years if deigned.
However there is a specific exception in part (9): A notice under this section shall not require the disclosure of any key which (a)is intended to be used for the purpose only of generating electronic signatures; and (b)has not in fact been used for any other purpose.
It seems therefore that a relatively easy solution if one was concerned about having to reveal potentially incriminating information would be to regenerate your keys every time you need them. According to this answer it is possible to build a deterministic PGP key generator. The seed that is provided to this would be a key that is intended for the purpose only of generating electronic signatures and has not in fact been used for any other purpose, which would appear to exempt it from required disclosure. This key could then be used to encrypt / decrypt any sensitive data, and disposed of when finished.
Would such a scheme protect against being required to provide access to such sensitive data?