No specific ban on bonfires in the UK but you could get into trouble, eg. by being a nuisance to a neighbour, smoke interfering with road traffic and burning plastics.

I did have a neighbour ask me to dampen one last year but that's very unusual (probably the only time in towards 20 years) and was caused by a strange change in wind direction and me not noticing what was happening. It's about 50m from where I was burning to their house and the smoke went low and in towards them.