do you want to have to divulge problem relationship with neighbour which may result in your house not selling for a very long time?
this seems to have become the go-to reason for suggesting that people just give into unreasonable neighbours... the legislation for this is designed for more serious issues than this...
if the OP wishes to keep her shed, then she is allowed to - that is not a neighbour dispute...
OP's neighbour: Can you take down your shed so that I can paint my fascia boards
OP: no thank you, I wish to keep it - but am happy to work with you to have scaffolding put up so that the fascia boards can be painted...
that is hardly the stuff of a neighbour dispute and most certainly does not need to be reported... along with conversations about whether the OP should share her last Rolo with the neighbour ;)
It is quite possible that the neighbour saw OP removing the rest of the shed, and assumed (wrongly) that the roof was also due to come down - in which case their request makes sense... but it is up to the OP - if she wants to keep it (and on the basis that it is legal etc.) then that is the OP's choice...
some of the comments on here verge on the ridiculous - do people really believe that someone should remove permanent structures on their land just because a neighbour asks them to, should the neighbour also choose model and colour of car the OP drives / the curtains she has up & her children's names - so demeaning for the neighbourhood to hear OP shouting for Jane to come in for tea - Persephone would have a much better tone to it... 