The old British rifles in this caliber were usually made with 25" barrels. That is because in the early days scopes were very rare and sight radius was considered important.
The 375H&H shell used it's powder quite well, and a 22" barrel does anything you'd need it to do.
I'd bet if you chronograph the rifle with a 25" and then cut it to 22" or even 20" you will find the loss in velocity is not enough to worry about. Heck, the old 375 H&H Flanged (used in doubles) was thought of VERY highely in Africa, and it was loaded with 270 grain bullets to only 2450FPS. No one ever said it was under powered.
I like my old classic 375 and I have a 25" barrel. I hunted with it in the Selway (and a lot of other places too) and in heavy brush I have not found it to be too long.
I have used that rifle more than any rifle I own except for my old Mauser in 270 winchester. My 270 Win is on it's 3rd barrel, and my 375H&H is on it's 2nd. I have use that 375 a LOT, and I never found it to be too long.
If you like a shorter barrel, cut it off. You woun't be sorry, but I doubt you'll find a lot of difference either.