The 77 Sporter has a muzzle diameter of 0.550 and length of 22" for most calibers, with some magnums, such as 7mm Mag and .300 Mag, having a 24" length (I don't have any magnum 77's, but someone can fill in the diameter info). The No 1B is a 26" barrel; which is much heavier (I don't have a No 1B, but someone can fill in that diameter info as well).
I've seen No 1 barrels on a 77 action; the threaded shank needs cutting down, and the stock opened up.
Going the other way, putting a 77 barrel on a No 1, could be lots of work...but is doable with $$$.
Ted