Answer
How high can a fence be without planning permission?
Up to 2 metres, but only 1 metre next to a road used by vehicles.
In short
You can build or replace a fence up to 2 metres high without planning permission, with one exception: next to a highway used by vehicles, or the footpath beside it, the limit is 1 metre. Listed buildings and some conservation areas are tighter. The same limits apply to walls and gates.
A note
General guidance, not advice. Rules vary by site, and Article 4 directions or conditions can change what applies. Check with your local authority and the Planning Portal.
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