Wow, first off, my memory is not that great, but for example, in the Shackleton era, there was invariably at least one, and possibly several, airborne in the sensitive areas around our coasts, checking for the presence of Russian submarines or surface vessels spying on any of our naval facilities. The Russians then, and possibly still, also had spy ships in the shape of fishing vessels permanently stationed around our coasts, two types I recall, were the Lentra and Okean.
I certainly consider myself very fortunate to have survived Shackletons, we lost something like 12, and many good friends, in the years that I operated them.
In the TV programme, they talked of the SOSUS underwater listening cable, (laid in the '60s as I recall, and not shortly after the war as implied) which worked well as far as I know, but as it was in a fixed position, it could only report boats (subs) as they approached, its range is still secret, and in the late Shackleton and then Nimrod era, we continually monitored the Iceland - Faroes gap with our underwater buoys, as this was the only realistic route for them through to the Atlantic. Our submarines were very good at what they did, but I can assure you that surveillance against Russian subs in the broader sense, could not have been carried out by subs alone as implied by the programme.
Unfortunately, your Government does not now see it as essential to maintain maritime security for us, an Island nation.