No, the expectation was that tactical nukes would have been used extensively in continental Europe as the Red Army advanced. The UK intention was that that they didn't get the idea of dropping them on the UK as well, either to take out the UK air bases (that "unsinkable aircraft carrier is I believe the US termed it) or defences.
(As an Air Defender sitting in one of the 3 bunkers thought to be on the first target list I heartily agreed with that idea)
So the tacit presumption was that if the Red Army used nukes against the UK, the UK would respond against Russia itself, with the only weapon it had guaranteed to be able to reach Moscow - Polaris. Which would inevitably lead to a full exchange of strategic weapons by the USSR and USA.
That being known, it could reasonably be expected that the gains of using nukes against the UK would be far outweighed by the consequences, and they would never be used.
The above was not some cunning ruse which the UK "put over" on the USA, Elmo. They had as little wish to lose their bases in the UK as the British. Call it a mutual agreement and one of the advantages of being both a very close ally and a nuclear power.