Whoever puts up a fence is perfectly entitled to put it up whichever way they like. There is no law.
However please consider the way that the vast majority of people would erect a fence if it was at the front of their property, bordering onto a public footpath. Almost everyone would erect it with the posts on the 'inside'. That has led to a convention (but not a rule) that people who erect fences between their garden and that of a neighbour also do so with the posts on their side of the fence.
No law about that .. but you should have the posts inside your land. One of the benefits is maintenance.
Align the outside edges of the posts just inside your boundary .. and no-one can complain about it.
Some people think of looks first, and forget about security. They'd rather look at nice smooth planking facing the inside of their property than at ugly posts. But if the posts are on the outside, it makes it far easier for anyone to climb over into a property, rather than having the fence act as a barrier.