I'd say bare minimum is:
Rack
Panniers
Tent
Mat
Sleeping bag.
Head Torch
We tour in Britain, mostly for weekends, there are pubs, cafes and super/mini markets everywhere. You don't
need a stove or cooking stuff although it means you aren't so poor in the long run. If you don't know if you'll like it, borrow stuff and see how it goes.
If you are anywhere near London, we can lend you
anything . When we met, clarion had 3 tents and I had 6 and we both had stoves, mats, pans, sleeping bags etc so we have duplicates of pretty much everything, except where we've upgraded and got 6 or so
.