I'll offer up my opinion...
I own two hifi setups - one worth around £1500 and the other worth around £500. The only reason I'm telling you this is because in 90% of the time they are indistinguishable. I reckon if you shopped around you could get a killer system for next to nothing.
Basics are a simple 2 channel amp (stay away from surround sound amps - unless you have a need for one of course). Cambridge audio, Nad and Denon are all good bets and all sell solid budget ranges. Personally I like Nads (I know...silly name) but they are typically low on looks but high in sound.
Old Mission speakers are good. New ones not so good. In recent years they have been reviewed badly. If I was to offer a budget speaker I'd personally go for Tannoys or Q Acoustics.
CD player - like amps Nad, Cambridge Audio etc are all fine.
You could always forgo the CD player and buy a music streamer (I have one, it's great).
All that said.....depending on your budget there are stacks of bargains out there, Richer Sounds and various other online retailers sell package deals. Typically these are mostly Amps and speaker setups.
Also. Don't forget Gumtree. Picked up some lovely stuff locally for next to nothing In the past (rega turntable for £75, and a CambridgeAudio CD player for £25)
Ps....BOSE (Buy Other Sound Equipment). As it happens I don't have much of a problem with Bose, but they are famous for not allowing their kit to be reviewed. On occasion though someone does purchase some of their kit for the purpose of seeing what the big deal is.... Rather predictably they often get okay reviews but more often than not the reviewer notes the overall quality of the components/and sound is much lower than what the cost of the item would have you believe....just a word of warning.