Having a brick skin on the outside is fine, but it is quite expensive, complicated and bricks are energy intensive in their production – cooked in a kiln with gas. Also the foundation would have to support the brick work as well as the timber structure, and since timber frames move overtime whereas the bricks wont, allowances have to be made around windows for this variation as per building regulations.
Alternatively, brick slipps can be used – these can be narrow, say 10mm thick, made from resin and fixed to the timber frame. Look-wise it is hard to distinguish them from real bricks. It is well worth seeing some installed to see how good they now are. Stone slipps are also possible, and they too are very convincing.
Images below of bricks slipps buildings are provided by Alsecco: