The general policy in respect to fencing and planning permission is relatively brief, albeit you should always check with your local authority or the government planning portal before commencing any project.
Fencing can usually be erected upon your property without the need for planning permission, as long as the fencing has a height of no greater than 1.00m (3'3 approx) to your front garden or 2.00m (6'7 approx) to your rear garden.
What else do I need to consider?
Other factors may also effect the style or height of fencing you could choose, such as any existing covenants that are bound to your property or any specific local area planning guidelines.
Speak to your neighbour(s) as it is a purchase that they will also be seeing for years. It's better to discuss and agree the style and height before purchase than argue with them afterwards.
Common sense and the nature of any existing fencing should be able to guide you in the right direction towards what's possible, but if you're in any doubt a phone call to your local Council Planning Office will ease your mind before you start work.