£350 is not a lot of money, but a good starter set might be the following:
Yamaha NSP240 speakers (5.1 with active sub) @ £79.99
Toshiba 350 @ £119.99
Yamaha RXSL80S @ £149.99
You could always swap the Tosh 350 for a Pioneer 575 (lose HDMI but still get prog scan through component, gain SACD and DVD-A playback) or a Samsung 950 (keep HDMI, gain SACD/DVD-A playback, but lose flexibility of speaker settings for SACD and DVD-A + add £10). Don't think the speakers will be up to replay of this calibre anyway, and software is limited.
All these prices are from RS - know that the Tosh can be bought cheaper. Only thing I have not heard is the receiver, but as a Yamaha, the processing is likely to be good, and should make a good match with the speaker set. Note: for this sort of money you are not going to get a top sound, but it should all be ok. Of course, this type of system is a replacement for what you've got, which may not be ideal.
If you are looking for just an amp and some speakers, Marantz amps usually sound very good with music, and you should be able to pick up the 5500 for quite a bit less than £300. The centre speaker presents a condundrum - might be hard to get something to match your floorstanders. A number of amps these days come with speaker and room equalisations (and not just THX amps), but I have no idea how effective they are. Plus, those amps/receivers tend to be expensive. The Pioneer 915 is such a receiver; it is 7.1 and does have both an automatic set-up and speaker equalisation, but it has not met with entirely enthusiastic reviews (can be picked up for about £250), due to a supposedly bright, thin sound. Might be worth auditioning with your kit though. Having a matched centre is important.
An alternative would be to buy an amp with two zones, and use a 5,1 satellite package alongside your current stereo speakers, switching between them for home cinema and hi-fi duties. You probably need to double your budget to get what you want with full size speakers, especially if you are not willing to buy second hand.
Hope this helps