The success of this effort presumes several things.

1) That the launch or release of a nuclear weapon is not detected en route to the target.

Satellites conspire with launch plumes, grounds stations with radar returns, etc. to prevent bolts from the blue. While UK/France might be getting their clocked cleaned, if the U.S. hasn't been nuked yet and won't get into the fight until it is, much of the launch detection infrastructure should be functional.

2) That the order to release nuclear weapons against a western country can be compartmentalized to the degree necessary to ensure no leaks, subsequent whistleblower activity, etc.

Nominally this would be a TS/SCI level order within the National Command Authority equivalent, but one person, perhaps of unwavering morale character, or grief over the loss of a relative living in the US, or the death of college roommates from a study abroad trip, could pop smoke on the true source of the nuclear attack.

3) That final attribution of the post explosion nuclear material following technical analysis isn't successful.

Here's an unclassified document from Los Alamos that provides a brief overview of nuclear fingerprinting.

https://www.lanl.gov/science/NSS/iss...ory2full.shtml

I would speculate that the capability to forensically study nuclear material for the purpose of assigning attribution to a nuclear explosion, likely existed prior to this publication, at an appropriate level of classification. While isotope signatures of Soviet nuclear reactors would be difficult to obtain (though invaluable and thus a prime target for collection efforts), it's likely that U.S. labs have data sets on UK/French reactors, garnered through a wide variety of mechanism (mostly academic).

Failure in any of these domains (and realistically, several others I've not touched on) would be a catastrophic event for the responsible country.