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As Timmy said only if it's over a metre, see:
http://www.planningportal.gov.uk/permission/commonprojects/fenceswallsgates/I looked into all this when we were planning our elaborate fencing project in the back garden. We decided that we wanted some of our fences just over two metres, but as we were putting in for planning permission anyway the architect just stuck them in his drawings.
I was amused to learn that the width of brick walls has to grow as you go further north (see the map on that page). Makes sense but just something I'd never thought about!
Do you need council permission to rebuild a front garden wall?
It's a bit premature asking as we don't even have walls or a floor downstairs yet, but I can see a new wall abutting the pavement could be a nice finishing touch one day.
How much hassle would this be?