hi mate, are you still after gear or did you get sorted out?
i ight have the necessary info you are after, as i spent months studying the market for cheap second hand-but good-stuff.
i also had a cheap all in one hi fi which was good, but i wanted something better, but without spending ridiculous amounts of money.
for turntables, i was recommended: rega planar, project, the dual cs-505.
for amps " " : rotel, arcam alpha, audiolab 8000a, creek, nad 3020.
for speakers: wharfdale diamond, mission, royd.
basically any legendary british or european stuff. all/most the brands mentioned are really good entry level gear that is well within your budget and you will be able to play about a bit with your budget. but bear in mind, if you go for a second hand turntable, budget for a new stylus and/or cartridge.
here's what i ended up with:
turntable: thorens TD166 mkvi BC (with rega RB250 tonearm) £155 from ebay (local seller just up the road)
new cartridge and stylus for above: audio technica AT-95 £40 (local shop.)
amp: integrated arcam alpha 3 in mint condition £46 (ebay, picked up from chorley)
speakers: mission 731 bi-wireable £35 from cash converters in wigan.
speaker cable: free from our carls shed
all in, about 176 quid. it sounds really crisp.
there's maybe a more expensive amp that i would have liked to have gone for, or splashed out on a better TT, or fancy speakers.
with your budget you have a broad range of choice and leeway and can really treat yourself
Thorens TD166 mkvi-Rega RB250-Audio Technica AT95, Arcam Alpha 3, Mordaunt short MS904, Glade Scented Candles & Nescafe vanilla/caramel/irish cream latte