Hello. The Access to Neighbouring Land Act 1992 entitles you to enter neighbouring land to undertake repairs to your property. This includes the right to temporarily move the fence. You should advise your neighbour that you have these rights and that you will go to court to enforce them if necessary. Hopefully that will be enough to get him to change his mind. However, if not you will have to go to court and apply for an access order. This could take several weeks to arrange, depending on the reaction of your neighbour.
I think you'll have to budget £2,000 to £5,000 plus VAT depending on the neighbour's reaction. Even if you are successful, you might not get these costs back if the neighbour had genuine concerns, rather than just being awkward.
It would all be dealt with at the same time, costs and the order. Best of luck!
No problem - please don't forget to leave a rating. Best, WB.