Thanks all, there's some brilliant advice on here, and that rotary compost sieve looks fantastic. All I need is some compost to sieve now!
Well, I've decided to bung the banana and citrus peels into the compost, together with all of the other stuff. One gardening book I've been looking at says not to bother with the accelerator stuff,as all it is, is the same bacteria that's found in horse poo (that I can get free from my local stables. I already know not to bother trying to compost perennial weeds, but I have been making nettle 'tea' (yep, it's stinky,but gets rid of nettles), thanks to watching Mr Bloom with the kids, I didn't realise I could put the stinky dregs on the heap, it all adds to the mix!
The same book recommends periodically testing your soil's PH, and if it's too acid, liming it (for growing veggies). That's why I'm trying to compost stuff, the soil we've got already is good, but could be better.
As always, some great advice on here, so thanks to everyone who's chipped in, thankfully the advice has always been similar (not half and half yes you can and no you can't!)
Flobear, thanks for your comment re my username! I will be pestering you next summer for chicken advice, Hubby has agreed we can have some next year when we move over the road (father-in-law's old house, bigger house and bigger garden than ours).