Crmcc, just seen your post.
There are three issues here:
Your neighbour has written a letter re the covenant. I would think it highly unlikely that he is the beneficiary of the covenant and (if so) he can’t do anything to enforce it. I would read the wording of the letter carefully, does it state anywhere that he is the beneficiary, he is more likely just trying it on and he will own his house on the same basis as you, as will others on the road who have built extensions.
You own the freehold, does the covenant in the leasehold link in with the same in the freehold deed, if not you are probably in the clear to build the garage. Solicitors might be nervous about committing to this advice as there may be other documents that contain covenants that you do not hold copies of and it is difficult to prove these issues outright.
The issue will no doubt raise its head when you sell the house however there is a type of insurance available to cover breaches of covenant, you could ask a solicitor if this would help your situation. On selling the house this would probably be accepted as covering the risk and whilst the cost might be used in negotiation the sale should go through.
Lots of guessing there but I think you would be ok. You need a solicitor, think of them like doctors, they provide advice but its not always right more an educated guess based on lots of experience.