Do trains need a signal to tell them when to go?
I don't know the true answer but general observation at Streatham and Loughborough Junction suggests yes they do.
My assumption is that the driver just looks at the clock and leaves if he is on time or late, he doesn’t have to wait for a signal to leave.
I’m no train buff but I’m sure I’m right in saying drivers are governed by traffic light-style signs as much as their schedule. For both operational reasons such as managing ongoing delays and changing priorities at junctions, and safety reasons if there are any obstacles, broken down trains etc just ahead.
I'm not a railway person, but to the best of my understanding -
the 'traffic light' style signals show stop / go / caution (yellow means the next signal is at red, two yellows means the next but one is) - and these apply to any train whether or not it's stopped at the station, and these are controlled from the signalling centre (these are mostly big, regionalised, largely computer assisted now.) broadly speaking, the track is divided in to 'sections' and a train can't enter any section until the previous train has left it. and there are interlocks built in to the system so that trains are not allowed to be signalled in to conflict with each other at junctions and so on.
some signals will automatically go to green when trains in front have cleared their bits of track, some require the signaller to do something to set the route up (e.g. where there's junctions and potential conflicting movements) - and how far in advance of the train being due they do that will depend on other trains needing to cross its path.
leaving a station after calling there for passengers is usually up to the train crew (suburban trains on southern / south eastern / thameslink are driver-only so there isn't a guard involved) - the driver will, at the right time, and when safe, close doors, check that doors have closed fully, and depart (or where there's a guard, they will close the doors, check doors have closed, and give a starting signal to the driver.)
there are a few stations where either some or all of the time (because of how busy the station is, or sharp curves that the CCTV system can't see round) a member of station staff on the platform will give a 'close doors' signal followed by a 'right away' signal (these are separate to the 'traffic light' style signal.)
but if the 'traffic light' style signal is at red, then the driver / station staff will not start the despatch process until the signal goes to a caution / green aspect.
there have been one or two accidents when a train has been started from a station when the signal has not been clear and nobody involved has noticed until too late.
plenty more
here.