This is less than an hour's work for a solicitor, so it's staggering that this profession still thinks it can get away with this sort of nonsense. Nevertheless what you have been quoted is high - I've paid around £350 a couple of years ago for something similar - but only because the seller's legal representative refused to deal with me as a 'non-qualified' person.
To answer your question, first a caveat - I cannot, of course, provide you specific advice. However my general advice would be:
If the covenant BENEFITS the land being transferred to you and it is of use to you in the ownership of the 'strip' you are acquiring (say it gave you right of way over someone else's land) then it is my understanding that the proprietor (your family member) can split the convenent benefit and transfer it onto you, whilst retaining the same over his retained land.
If the convenant BURDENS the land owned by the family member, he/she would be well-advised to ensure transfer of the convenant onto you to bind you to it's limitations. This is of course essential if it something like a right to run pipes under the land and you will end up owning a section where the pipes run.
The covenants are not automatically transferred - look at section 12 - Additional Provisions. This is where the wording goes.
Finally, I believe that you should provide a minimal consideration for transfer of the land - £1 should do it.
The LR are quite helpful in dealing with laypeople - phone and ask them - though they won't provide you with specific advice.