The take away here, and this is really true of any country, not just the UK, is that it's a bad idea to suggest you're doing anything that could be construed to be paid work. I can virtually guarantee that if I turned up at the US border on a visa waiver and said I was a musician playing a few gigs they'd send me off for a secondary questioning at the very least. I wouldn't be surprised if I was refused entry.
The return ticket doesn't really factor into it: whether you're entering the UK, US, wherever - generally if you're going in on a tourist visa / waiver you can't work. And unless you have some documentation indicating your gigs are unpaid, you've only got your word...which isn't worth much.
The problem came because on the visa form it said occupation and singer was put down. When asked why she was there, she said holiday. Then being too honest when asked, she said she had some small non-paying gigs. I can understand how this might lead to secondary inspection but after phoning the venue (who told her they were non-paying, small and promotional) the immigration official went off on a lie claiming she knows how many thousands of pounds my friend was going to be paid and that they were big events (small open mic at a pub where my friend could do a few songs for London friends). The woman even admitted to me hours later that she made a mistake but claimed she couldn't reverse the paperwork.
With the US it's been fine for me to go over and work as a technical trainer in our US office for a few weeks at a time, but I declared everything on the VISA waiver.
I'm not sure on the specific rules for the UK, but yeah 'I'm going to play a few gigs, but, uh, don't worry I'm not getting paid for them' probably is a bad thing to say.
The return ticket doesn't really factor into it: whether you're entering the UK, US, wherever - generally if you're going in on a tourist visa / waiver you can't work. And unless you have some documentation indicating your gigs are unpaid, you've only got your word...which isn't worth much.