The UK system sounds back-asswards, but it strikes me as a surprisingly sane set of checks.
Man vs Machine has always been a royal navy doctrine. The US teaches nuclear engineers how to drive a boat. The UK teaches sailors how to run a nuke. Similarly, if the boat has to maintain independent firing capability (the whole point of the deterrent being in submarines is to avoid command&control decapitation), then any access control is a formality. If control ultimately falls to the crew, then don't pretend it doesn't - focus on the men.
Radio 4 sounds anachronistic, but it's a UK-based, govt-controlled transmitter, independent from military systems, which broadcasts every second of the day during routine operation - and because it's still cranked out on longwave (198?khz), can be heard across our waters & much of the north atlantic (the stomping grounds of our deterrent).
While civilian maritime broadcasts would sound like a more sensible failsafe, most of them are either broadcast or controlled from Northwood, so they're not independent of military systems, and are routinely silent between scheduled broadcasts.
What I do find interesting is the actual point of checking for civilian broadcasts - given the loss or failure of command&control communications, the result isn't a railroad to Armageddon - they're expected to implement some common sense. Compare this to the scenes in Crimson Tide, where Gene Hackman prefers blind obedience to the Protocol ..
And "hand-written" is a red-herring. The actual detail here is that only the PM ever knows what went in that letter once it's sealed. They don't have to be hand-written, and probably aren't anymore - but traditionally this was a side effect of not dictating to a secretary/typist.
Command and control is very hard: being able to always and immediately launch a nuclear attack but never subject to an unauthorized launch presents a variety of challenges. PALs help with the latter but not the former. Maybe because the Brits have fewer warheads (and therefore the ability to exercise more control) or needed to respond faster (being closer to the USSR and other nuclear powers), they made a strategic choice to skip PALs. Eric Schlosser's book Command and Control is worth a read if you are interested in the history of the US nuclear arsenal.
It was a hedge against a decapitation strike and the chaos that would result in the Soviet military due to its officers habitual deference to central authority.
Boy am I glad that project never got off the ground. A MAD-gap/race would have been terrifying.
A plane that can circle the Earth 4 and a half times is pretty cool, but at the cost of irradiating the whole planet? Maybe not so much.
http://en.wikipedia.org/wiki/Dead_Hand_%28nuclear_war%29
It may still be operational, but not normally turned on - for obvious reasons....
At the other end of the spectrum the UK has no automated control preventing unauthorized launches (no Permissive Action Locks) and we check to see whether Radio 4 is still broadcast to detect whether civilisation has ended and hand written letters to instruct the captains of our Tridents subs what to do in that event.