This isn't really likely in the most of the UK but I lived in a remote area on a group water scheme in another country until a couple of years ago and our shower used to loose pressure when running on hot.
First of all it was fed from a tank in the loft so make sure that your tank is filling properly if this is the same setup for you. then my problem was that the filter was getting blocked up with silt and weed as we got our water from a lake and it wasn't filtered.
As I say not likely with Thames water or the like but keep it in mind. If it is doing this then the temp will rise compared to where you have set the knob over a period of time, so you will find its hotter at a lower setting but less water flow. our man Rich above is likely to have the more likely answer though.
Another possibility in hard water areas is that its just scaled up. This will mean it takes longer to reach temperature and the controls will slow the water down until it reaches the required temp.
If this is the case and you really feel like messing about for an afternoon ( wet, nothing on telly, all pubs in the country on strike, missus giving you funny looks) you could remove the wee boiler and try to descale it either with the citrus acid descaler you get in the shops or with a strong mix of lemon juice and vinegar but FLUSH IT OUT AFTERWARDS. Like I say really messy.
Good luck
Kenny F
October 2008