It was two things.
First, the FVP 4000T can definitely be sluggish, especially after just bringing it out of sleep.
Secondly, the FVP 4000T got much better 
when I opened up the remote control and cleaned the rubber key contacts. I had not realised that the red power light was sometimes not coming on when I pressed a key. Also, on careful testing, a successful key press was very dependent on whether I pressed exactly centrally on the key or pressed off centre.
See Disassemble remote control to fix intermittent keys where I stripped and cleaned it and added sticky-backed-aluminium foil to the keys. It looks like just cleaning the accumulated greasy gunge is all that is necessary.
After doing it all keys are crisp and responsive - it now works a treat.
