If it says “any permitted” then it’s valid on any route defined by the routeing guide, not by any route you happen to fancy.
Manchester-Bristol “any permitted” is valid on routes shown by maps
at
https://rgpp.iblocks.co.uk/maps
which do not include London.
It also happens that Sheffield-Bristol “any permitted” is not valid via London either. However there’s a separate “+VIA CHESTERFIELD” fare available, in which the “+” means including London Underground via London. So the “not via London” fare is to differentiate it from this.
See
https://www.brfares.com/!expert?orig=SHF&dest=BRI&period=20260113
Manchester-Bristol has an alternative “via Hereford” ticket, but none “via London”.
EDIT: I was wrong,
@AlterEgo is right, Sheffield-Bristol “any permitted” is valid via London. The problem is, there’s no “any permitted” ticket available other than singles priced by LNER. See
https://www.brfares.com/!expert?orig=SHF&dest=BRI&period=20260113. The answer to your reasonable question is not simple.