The really early Yamaha receivers are stonkingly good as stereo amps thanks to the prodigious power supply, low noise floor and excellent headroom. DSP-A1000, DSP-A2070, DSP-A3090. All of these will easily deliver 4x80W or 5x80W and more, all channels driven, 20-20,000Hz, continuous RMS and at very low distortion figures.
Without getting too technical about it, it's the power supply, reserve capacitors and output transistor combination that sets the fundamental character of an amplifier. The power supply converts mains 240V AC in the lower voltage high current DC required to run the amp. The bigger the power supply reserve capacitors then the smoother the DC power rail (less ripple = less audible distortion and a lower noise floor which gives a better signal to noise ratio), and then lots of high-current output transistors that can deliver huge gobs of power when required without overheating means very low signal distortion even at high output levels. All combined, this gives the amp the ability to drive even difficult loads very cleanly and still retain a healthy margin above the rated power. This is the Dynamic Headroom. It's what makes some amps sound effortless and seemingly limitless on power where other amps struggle and become brittle-sounding as distortion rises when they're trying to deal with a dense or complex mix.
A small number of the later Yamaha AV receivers pull off the same low noise floor feat but on a smaller scale. DSP-AX620 is one.
There were a few DSP-A3090s on Ebay recently. Condition can be variable. Battered examples lacking remote, accessories and box can be had for under the £150 mark. Some chancers try it on too. I've seen less-than-tidy examples advertised at over £400 on a BIN. There was a very tidy example complete with box, manuals and remote that sold for £265. With carriage @ £33 (it's a heavy mutha at 21kg before packing) that would have tipped in just under your friend's £300 budget.
To get similar power levels and performance with a 2-channel Hi-Fi amp you'd have to spend a lot more, even second-hand. I'm thinking Krell K-300i (2 x 150W @ 8 Ohms) used for approx £1,000-£1,500, or the Musical Fidelity M6si at 2 x 200W @ 8 Ohm at north of £1,500 used.
If you don't need remote control and can get around the need for Optical in by using and Optical to Analogue converter then there's an Audiolab 8000LX stereo Hi-Fi amp that would be a nice buy. 2 x 60W but lots of current so far more potent that the headline spec suggests. It's sitting on the bay at £150 with 0 bids and 16 hrs to go. Collection only by the look of it. It's not a great Ebay listing.
I know of a DSP-A2070 that might be going on Ebay sometime soon. This doesn't have Optical in, so you'd need one of those £10 Optical to Analogue converters, and the amp is Dolby Pro-Logic only. Still exceptional for 2 channel stereo though.