You would naturally think not. Surely a zealous walker will have a field day in a court of law?
The fact is however erecting a gate does not necessarily amount to an interference with someone's right of way.
It all depends on the gate in question.
Erect a gate which is unlocked and you are probably fine. The legal test is as follows: "can the right of way be substantially and practically exercised as conveniently as before?"
In answer to that you would be hard pressed to find against a single unlocked gate.
Clearly a locked gate would fall foul of this test. However, what if you gave a key or fob or code to people benefiting from the right of way in question? Surely then you are ok, right?
Well actually the answer is probably no because you are still obstructing visitors, emergency services and deliveries. Quite how a case in these particular circumstances would come to court is a moot point however.