Had fun doing this (at work, with literally no work to do for literally the first time in my life) as I've never counted or listed my rivers before. My list is a bit false as I do get around a bit, go camping for reasons other than fishing, but take some gear with me, and I do tend to fish tributaries that are available on the same ticket as the bigger river, just for the sheer love of rivers and to explore something new, so the rivers marked* I have fished for a few hours only, and pretty much always blanked on all of them. But, FWIW, in the last 6 years since I've been back fishing, I've had a go at about 24 rivers but have only caught barbel on the 8 rivers marked "B."
Adur*
Aire B
Arrow*
Arun*
Avon (Warwicks)
Calder
Cod Beck* (Swale tributary)
Dee*
Holme* (Calder tributary)
Lugg* (Wye)
Monnow* (Wye)
Nidd B
Ouse (Yorks) B
Ribble*
Severn
Shannon
Swale B
Teme*
Trent B
Ure B
Vyrnwy*
Wharfe B
Whitham*
Wye B
A false list but not too bad, makes me realise I'm v. lucky considering I don't drive.
When I was a nipper in the seventies, I fished up to the age of 15/16. Mainly on summer hols and again not too bad considering no family members and nobody else I knew was into angling:
Blackwater (co Cork)
Brosna (co Offaly)
Conwy* and other Welsh rivers
Dee
Lee
Nith, water of Fleet and maybe some other SW Scottish rivers
Shannon (various stretches)
Suck (co. Offaly)
Tamar*
Weaver (I didn't know at the time that this was the river my ancestors lived and worked on for centuries - it was literally the river that put rivers in my blood)
Wyre (Lancs)
Between the ages of 16 and 50, I had a sum total of about 10 fishing sessions, always on hols, on these rivers.
Don't think I ever blanked though I also never caught anything impressive:
Aragon
Cam/Granta/Ely Ouse
Dordogne
Nile
Po
South Tyne
Thames
Vézère