You won't need planning permission to erect a fence unless it is higher than 2m (6ft 6in), your boundary adjoins a highway (when you may be limited to a 1 m/3ft 3in high fence), or where your area has been designated as 'open plan' (in this case you may be allowed to erect low 'decorative' ranch-style, or post-and-rope fencing). Short term, a fence will be cheaper than a masonry wall, but you can argue that long term, the cost of maintenance and eventual replacement will cancel out any savings made. Nevertheless, a wooden fence that has been treated with preservative regularly should last for years.
Picket fencing (pictured top left) is low level and 'see through' and is good for boundaries or at the front of a cottage-style garden. Narrow, vertical 'pales' with a rounded or pointed top are spaced evenly at 50mm (2in) centres. Picket fences are difficult to make by hand but fortunately are available as prefabricated panels constructed of softwood - or even plastic.
Trellis (top centre) is lightweight but does make a good windbreak and can offer privacy when climbing plants have grown over it. The concertina fold of trellis, formed from thin lathes of cedar or other softwood will only be as strong as the posts and rails that support it.
Close-boarded fencing (top right) is ideal for screening off a garden or boundary from an unsightly road or neighbouring plot. A close-board fence is made by nailing overlapping featherboard strips to horizontal rails. Featherboards are sawn planks that 'feather' or taper across their width from 16mm (5/8in) in the middle, down to around 3mm (1/8in) at the edges.