That's a bit over-reaching.
Involved? Yes-ish, to some fairly broad extent.
Instrumental? Nah, that's perhaps going a bit too far.
Critical? In the sense that he was an advocate for "letting refugees in"? Yes, he took part in the process.
His negligence and narrow-minded activism, and the negligence bound to his activism and policies, are responsible.
So are the people who voted for him, however.
But now that the police is cracking down on anybody voicing outrage/concern or any kind of milk-toast take on the matter, it is only a matter of time before it is treated as yet another Russian/Far Right/MAGA/etc... ploy to destroy the fabric of the UK.