I posted the above topic and had several very helpful replies so I thought I would post an update.
I gave up trying to fix the problem myself and gave the bike to our local independent BMW mechanic.
He had another K75 in for mechanical repair so he swapped the Electronic Ignition Unit and the EFI Computer.
He then checked the Fuel Pressure, Fuel Injectors, Water Temp Sensor and Air flow Meter with no improvement.
The bike was left for a few days then it started and ran normally, starting every morning for 5 days then went bad again.
Swapped the Fuel Tank over and finally the Air Flow Meter at which point the bike ran ok again.
The conclusion is that it was an intermittent fault in the Air Flow Meter although this is not 100% definite.
It has started every day for about 10 days now and has had a 20 mile run in the rain with no problems, in fact its like a new bike, as the timing has been reset and the injectors balanced. The throttle response is now immediate and the engine sounds super smooth.

It's good idea to post this with your original post so we can the initial problem.

Good to hear you got it sorted and the bike is running nice and smooth.