With any type of construction work, the standard advice is to get at least three quotes and I'm sure that will be equally sensible with your fencing requirement.
I suggest that, as well as the local one-man firms, you get a quote from at least one of the 'big boys' in the business. Sometimes they can be a lot dearer than individual traders but this isn't always the case. You'll also know that you'll be dealing with a firm which specialises in fencing (rather than with a general builder, gardener or handyman).
My suggestion is to try Brian Noble Fencing:
http://www.noblefencing.co.uk/
(If you click 'Product Guide' and then select 'Wooden' you'll see examples of the types of residential fencing which they can offer).
Chris