The biggest question is - do we have to include Egypt, Israel, India and Pakistan? Because those are problems (closing Suez and, well, nukes, really). South Africa (for the ability to deploy mines around the Cape) and Iran don't help.
It would be a very brave President who would start a war with the UK without seeking to neutralize its deterrent. And you can't go after somebody else's nukes half-heartedly - there's too much of a chance of a "use it or lose it" reaction.
Opening 5 minutes of the Anglo-American war will be a US sneak attack that will make the infamy of Pearl Harbor look like a drop in the ocean. Nuclear-tipped torpedoes launched against the patrolling SSBN(s) (and the war can't start until they are found) will be followed by radio buoy deployment by the attacking SSNs to trigger SLBM strikes against Faslane/Rosyth, Aldermaston, and Porton Down, and possibly some other sites (not sure about Portsmouth, Devonport, Barrow, Sellafield, that place off the M4).
Conventional A- or SLCM strikes against St Mawgan, Fylingdales, Vagar, Saxa Vord... I'm not sure what air bases haven't been closed - I think they've shut Leuchars & Kinloss - maybe Stornoway and St. Athan? Not until those go in will a CVBG contest the airspace over the UK.