In my experience commuting on trains from all over the country - Scotland, midlands to South East overcrowding can happen anywhere that a short formation is provided compared to the usual service. But those occasions aside the worst by a long way is the South East round London (no surprises).
Worst offenders - Waterloo-Woking stoppers, and on the same line, the Clapham Jct-Woking-Farnborough-Basingstoke semi-fasts are rammed at peak hours too. Moorgate services are comically full at rush hour, Anything round Richmond can be pretty bad too. Cambridge trains from KX are often uncomfortably full. Victoria and Waterloo stations in general are overcrowded!
Away from London, Glasgow-Ayr services can be very busy around 5pm (esp on Fridays), Cross country on sundays (just about anywhere!), and the Bath-Bristol services are under-equipped for the number of people on them.
BUT - none of the above compares to the british holy grail of overcrowding - the Tube. I work in the city and the most notorious lines that I avoid (if possible!) at rush hours are Vicky line between Victoria and Kings Cross, Northern Line round London Bridge and Bank, Waterloo and City line (if you can even get on to it!), Central Line through Zone 1, Circle line (Paddington to KX and around Monument) and the Jubilee line between Waterloo and Canary Wharf.
The worst overcrowding I have ever seen wasn't Japan or NYC, it was the Victoria Line, on a Friday at about 6pm just before Christmas in 2005. I remember it vividly - They'd closed the gates at Oxford Circus to prevent a crush developing down the stairs, but the escalators were still piling people down to the tunnels and platforms that were full to bursting. They had to hit the emergency stop on the escalator to stop people ploughing into the backs of the crowd waiting for the platform. To make it worse, everyone seemed to have either suitcases trying to get home for Christmas or bags of christmas shopping. After waiting for about 15 minutes I got on a train to Kings Cross where it took AGES to get up to the mainline platform because of queues at the ticket barriers - TRYING TO GET OUT!!! God help them if there had been a fire down there, while I'm sure the exits and procedures are adequate, it's the mass panic mentality that would worry me.
So there - that's my 2 cents worth.
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That could work, the platforms at Winchester could be extended in both directions with some minor work (not too sure about the bridge in the Eastleigh direction though).
Hmm. Don't think that would be a good idea. Winchester is a "change to nowhere" station. Basingstoke would be a much more sensible bet. Platforms 1-4 could be extended to the south/west over the road bridge (which is actually a tunnel underneath), then you'd have a large station involved in the process - one where people change between London/Southampton/Bournemouth/Portsmouth/Salisbury/Reading/"The North" etc...
Winchester serves itself well, but nothing else.