My Golf runs fine when it's cold.

Hi,
My golf runs fine when it's cold, but once the engine warms up (maybe 2 - 3 miles) the engine starts skipping, and acceleration becomes very poor, and almost like it's struggling to get fuel. At low revs the engine often stalls, and is very difficult to start again - the engine turns over, but just won't start. Also, if running at say 60 mph, suddenly it will lose revs for a split second and really jerk around. All very odd, as it runs perfectly when the engine is cold. All of the above problems only happen when the engine has warmed up.
My local garage has replaced the fuel pump, but it made no difference so am reluctant to take it back there - they clearly don't know what to do.

Help!