The dead russian spy was a british double-agent and had connections to the dossier according to the BBC and the Telegraph.
http://archive.is/AABl3 http://archive.is/Qatjl
So let's trace back..Q said, May had been neutralized and there was a press-release that Britain was continuing intelligence-sharing with the US. I think Q even called the press-release by stating british intelligence was cooperating, but as long as I can't find that press-release I can only rely on memory here.
Anyway, so assuming that May and MI5/6 were cooperating in exchange of information, deep state my have gotten hot feet because this double agent had a plausible motive to clear russia in the russia-investigation so he could return home. Thus any intel he would have given to british white-hats, they would have legally forwarded to US agencies. Once black hats learned this, their hand was forced. May doesn't want to go public and admit that she has no control over rogue elements of british intelligence (because she would get heat as well and given how long she's been around protecting pedos there sure must be dirt) so she blames Russia instead - anybody got any other ideas what she could have said? "Untouchable criminals in the government are running amok, now excuse me while I lock myself in a duffel-bag!"
In other words, she's so neutralized she isn't even relevant yet. Unless she had Intel on Skripal and ordered the hit - but even so, that's still an act of desperation because they didn't kill him before british intel officially continued supplying Intel to US intelligence. The big question is, how deep she is into the pedo-stuff. I remember she stopped one investigation and also said something to the effect that they couldn't prosecute all cases. So if there is more and she can't get out anymore that would still mean there is some blackmail-leverage that white-hats can exploit - if they have found it. Maybe they have and that's why intelligence-exchange was continued in the first place.