That's interesting. What is the purpose of these overspeed tripcocks in the platforms? Because in theory everything should stop there?
There's no such thing as an "overspeed tripcock." On conventionally signalled lines there are speed controlled trainstops ("sleeping policemen") to protect the overlap even further; there's one of these at Leicester Square Eastbound on the Picc and one on the District at West Ham Eastbound. Other places use draw-up signals to pretty much the same effect, although there is a visible signal. TETS (Trains Entering Terminal Stations) and TES (Trains Entering Sidings) are variations on this for trains approaching buffers.
To add further detail, some station starter signals, even automatic ones, are red, and then come off time occupancy of track circuits (provided the section it is protecting is clear!)
The reason for the 5mph limit is as pointed out by someone else; to protect the overlap should a train pass the signal at danger. Unlike on the mainline, signalling on the Underground is designed that should a train pass a signal at danger (assuming it isn't speeding, and everything is working correctly), it will stop within the overlap. Some stations the speed limit is higher, for instance Piccadilly line trains can pass through stations on the fast lines between Ravenscourt Park and Turnham Green[/Chiswick Park] at line speed (45mph) and on the local line at 20mph. There are other examples, details of which are contained within the line supplements.
Hmm. It doesn't slow to 5mph but it definitely slowed down through Tufnell Park.
Northern line isn't conventionally signalled so there is no need to slow down to 5mph. On the Northbound trains still stopped and the Train Operator had to press ATO Start buttons again; the reason for this was explained to me but I have forgotten.
I took a picture of a sign on a Victoria line platform (attached) which shows the limit there to be 30kph.