I recently bought a Rico Graftonite Bb Clarinet mouthpiece in size B5 mainly for jazz work. These are no longer made I gather, so it was an NOS (new but old stock). Earlier I bought a Bari Esprit mouthpiece, but it's tenon is of a slightly larger diameter, which did not fit the barrel of my Boosey & Hawkes Edgware intermediate clarinet. The Graftonite fits.
I heard on the various woodwind forums that the Edgware was considered the poor "Ramen eating"
(new term I learned for a starving musician) 
clarinet for a saxist to use to double on, because they are large bore and sound overall decent, but can be had for a few hundred dollars or less in decent condition.
Here in US they seem less popular, so I am game for cost effective instruments, being fully retired as of 13 years ago. My E-Bay purchases (US prices): $50 (2015), $87 (2020), $120 (2025).
This 3rd one I bought earlier this year is in all Grenadilla wood and is in the best shape,
(you get what you pay for), so I plan to have it serviced by Tarpley's Music Store in Lubbock, Texas. The other 2 I'll get around to it down the road. The bargain one for $50 needs considerable work, the $87 needs some but not bad. Interestingly these 3 have different body materials.
Now that I have a true Grenadilla wood one after 50 years,
(I was a clarinet player with the 264th Army Band, Fort Shafter, Honolulu, Hawaii, played a wood Buffet then), come to realize that with TLC required of wood, the "ebonites" (plastics) weren't bad after all. The Reserve Bands aren't funded as well as the active Army. Back in 1986 I was issued a brand new Selmer Bundy plastic clarinet. It was the first clarinet that played well in tune, better than the early Buffet professional one.
Active Army, we were issued 2 instruments, a pro model and a beginner model. The beginner model was for venues where one did not want to damage the professional instrument, like outdoor gigs - street parades and sporting events where there was possibility of rain.
As a band we sounded good in either, people couldn't tell which instrument we were playing.
Anyway, it will all come back to you, like riding a bicycle. Good luck!