I seem to remember seeing a documentary about the Falklands affair, in which a Foreign Office Minister from 1982 (David Luce?) stated that in his view the worst thing to happen in the crisis was the press getting hold of the news that three SSNs were being sent South. Why? Because it told the Junta that if they were to act they needed to before the submarines arrived.
We may have a similar number of SSNs now as we did in 1982, I suspect someone else will be able to say for certain. However we also had quite a few diesel electric boats, and they did a lot of routine tasks. Now all tasks have to be handled by the dwindling SSN numbers (to be reduced to eight) and the force is rather busy. Relying on being able to suddenly deploy three to the South Atlantic seems risky.