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.
“Many ‘political Islam’ movements share our values, say MPs,” by Tom Peck, Independent, November 6, 2016:
The government should narrow its definition of ‘political Islam’ and recognise that many Islamic political movements share the same values as Britain, according to a report by an influential committee of MPs.
The report criticises th [sic] Foreign Office for using the term to describe both groups that embrace “democratic principles and liberal values” and others that instead hold “intolerant, extremist views.”
It was also heavily critical of the FCO’s recent report into Egypt’s Muslim Brotherhood, which was conducted by Sir John Jenkins, while serving as British Ambassador to Saudi Arabia, which gave the impression that it could have been influenced by a foreign state.
Chairman of the Foreign Affairs Committee, Crispin Blunt, said: “We absolutely agree with the FCO on the need for a nuanced approach to the broad phenomenon of ‘political Islam’. We only regret that this approach does not appear to have been applied to the Muslim Brotherhood Review, which failed to mention some of what we saw as the most elementary factors that determine the group’s current behaviour.”…