UK Traffic Law
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What grounds were you thinking of?
When you say cross over you means a dropped kerb?
Do you dispute that there is no 4.5 m from the front of your house to the edge of the pavement?
Well, probably because they didn't give truthful information. Or maybe that the rules have changed.
You may as well appeal. It won't do any harm. The problem is that they are trying to avoid overhang onto the highway which would amount to causing an obstruction. That is a criminal offence and that gives them the justification for their position.
Appealing is all very well but the issue should not really centre wholly upon the unfairness of the situation. A better point is that over hang will not be an issue if indeed it is not for your neighbours.
Can I clarify anything for you?