It all depends on what one thinks “British values” are. If they include the denial of the freedom of speech, the institutionalized subjugation of women and non-Muslims, and punishments such as stoning and amputation, then yes, many “political Islam” movements share British values. But if British values have anything to do with the values of a free society, then this report is howlingly false.
There has never been a state constituted according to the principles of “political Islam” that wasn’t authoritarian, Islamic supremacist, oppressive, misogynistic, and intolerant. Kemalist Turkey, you say? Kemalist Turkey was based upon a rejection of “political Islam,” not some benign version of it.