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If you have a right of way over the access area as you state then the gate is permitted to swing both ways. This is part of the right of way and must not be obstructed by the other party. I hope that this helps and please rate 4 or 5 stars.
I am a lawyer and I can simply point out that any obstruction of a right of way is actionable in court by way of an injunction and damages. You can get a local high street solicitor (we can not do this) to write a letter confirming this to your neighbours and the cost would likely by about £100 plus VAT. Happy to discuss and please rate 4 or 5 stars for my time.