Upvote:5
The UK and Isle of Man form a Common Travel Area. There is no passport check between the UK and the Isle of Man. Moreover, you will always arrive in the mainland UK if you are travelling to the Isle of Man, so any visa issued should give you at least transit rights to visit the UK. Visas for the Isle of Man are issued through UK visa offices. You need an Isle of Man visa as the UK visa does not automatically give you the right to enter the Isle of Man
So in short, it's almost certain that your Isle of Man visa will give you the right to visit the UK. And in any case nobody will check your passport between IoM and the UK. Your visa will probably spell out your entitglements. If you are still in doubt, check with the office that issued the visa.