Are you seriously saying that a soundbase will beat the "QA 2000 package for 399" and a second hand AVR for £100?
Please go educate yourself
Don't be so condescending!!
My brother works with this stuff day in day out and we often spend hours after the store closes checking out the latest setups, different options.
I will reaffirm that in situations at home that having a soundbase system can at times give better results than a 5.1 full system although would always advice to get a soundbase that has a separate sub for more obvious reasons. This comes down to the space and shape of the room because if the room is too small then you will never gain from the system and you will find sounds are fighting each other and feeling muddled when playing.
The QA 2000i 5.1 is a great system. Yes it will be a level above the soundbase in terms of sound/performance however it requires setting up correctly, stands for the speakers, cables etc.
So lets add the QA3000 stands which will require 2 pairs at £99 a pair or 4 QA2100 wall brackets at £18 for each.
Then chuck in the cabling which OK doesn't have to be expensive however it is still an added cost of say £80 (some places may chuck in cables for free if you ask).
Then as you say you are onto a 2nd hand amp such as the Pioneer VSX-923 at the lower end of the scale but an ideal partner to the QA 2000 series which comes out at £150 ish 2nd hand.
Other options depending on how warm the OP wants the sound:
Denon 1910 £150 2nd hand (warmer sound)
Onkyo TX-SR607 £100 2nd hand (harder to find and closer to Pioneer in sound)
Sony STR-DA2400es £100 (for me the weakest of the options but could everyone different with sound)
Steps up but worth the money if you are already looking at the 5.1 system
Onkyo TXNR 616 around £250 2nd hand but a superb amp for the money.
But yeah all in you are looking at £710-£850 for the speakers/amp setup so the soundbase is under half the price and not expecting to compete but does come in on budget at least from initial stated budget.
Now if the OP is as they say happy to go up and the room is at least 4m x 4m (really want a room this size to really get the speakers to work well in surround sound) then yes the QA 2000i 5.1 speakers make sense. I would personally be looking at buying new and seeing what deal the OP could get on a full setup (often offer 10-15% discount and/or free cabling when buying a package):
QA2000i 5.1 set £399
Yamaha RXV381 £219
Cambridge Audio Symphony 300 Cables (assume 3m for fronts and 8m for rear) £53
Cambridge Audio Banana Plugs for cables £25
Cambridge Audio AUD500 7.5m Sub Cable £30
Wall mounted brackets for the 4 satellite speakers £72
Total cost £798
I would push for the cabling to be free (with above spec) or 10% off depending on how things seem to be going making it around the £690-£718
Again this is assuming that the room is around 4m square (ideally you don't want an exactly square room) but just area wise. It would be best if the room was really 4m wide by 5-6m deep but you would need more cable length then.