Julian Cope directly referenced this little-remembered, hard-to-fathom episode in late Clash history—from the period after Mick Jones had disastrously been removed from the band—with his three-day “Joe Strummer Memorial Busking Tour” in October, 2008. (Check that tour’s impressive itinerary here — then search youtube to see video highlights — there are many).
I’d love to know more about The Clash’s tour (are there any videos? etc). For now, though, there’s this…
From Passion Is a Fashion: The Real Story of The Clash by Pat Gilbert (2004), p 352-3:
In May 1985, [Clash manager] Bernie Rhodes, [manager] Kosmo [Vinyl] and Joe [Strummer] devised the Clash’s last hurrah—a busking tour of Britain. The idea was that the group would assemble at [guitarist] Vince’s flat, leave their wallets on the table and hitch to Nottingham with a few acoustic guitars. They’d then see where the wind would take them. Over the next two-and-a-half weeks, Britain’s provincial towns and cities were thus treated to the extraordinary sight of The Clash popping up under railway bridges and in subways to entertain them with Monkees, Chuck Berry, Eddie Cochran and Cramps songs.
The group kipped on fans’ floors and in cheap B&Bs. They survived on the money thrown into their hats. It was a genuinely exiting and unpredictable experience. Joe described it as ‘the best tour we ever did.’
Paul [Simonon] agrees. ‘It was like starting out fresh again,’ he says. ‘It was great. “We’ll meet you in Glasgow in a week’s time,” and the idea was to leave everything behind other than the guitars. You couldn’t take any money with you. We survived by our wits. It was as exciting as the Anarchy tour, you never knew where you were going next. I remember we were in Leeds, it was 2 a.m., and it was outside this black club, and people were coming out and really digging us. There were two white guys and they were shocked it was us. They said, “Where you staying?” And we said, “We’re not staying anywhere,” so they invited us to stay at their mum’s. The money we made from busking meant we could go further, we didn’t have a plan of where to go next. There was no rules. You didn’t have to be on the so-and-so plane at twelve o’clock.’
Arthur Magazine 
I saw them on this tour, on a late night National Express from Nottingham to Leeds- it was very exclusive- just me, them jamming at the back and the coach driver. Unfortunately I wasn’t into the Clash much then, so didn’t recognise them. I only realised a few days later when there was a report about them busking outside an Alarm Leeds Uni gig in the Uni newspaper. The Alarm came out to watch apparently.
There are, to my knowledge, about 4 separate recordings of these gigs. While all good, the best on sound quality is the Station Pub gig. Worth seeking out.
Please check out Joe Strummer Slept Here: https://www.youtube.com/watch?v=txZmfG2t3Eo
Myself and some other local musicians have been recreating those gigs in Glasgow venues, as The Strummers. All money raised (passing the hat) goes to the Joe Strummer Foundation.
I was at the Leeds busking outside the Royal Park pub, then when up to the refectory which they also played outside . It was amazing people were literally running from student house to student house telling us all . No mobile phones back then!
I was working in Nottingham at a casino – start of the shift we’d have to take the previous nights takings across The Old Market Square to the bank. When we came out, I noticed that there was a large crowd around a couple of buskers – when I got closer I realised that it was Joe & Paul on a couple of acoustics. I’d seen them on the “London Calling” tour back in 1980 & wanted to hang around & watch them, but we had to get back to work. Last time I saw them – RIP Joe