There are untold numbers of rabbit breeds. For older British patterns, it can safely be assumed that a wild British rabbit Oryctolagus cuniculus - Family: Leporidae is meant.
http://en.wikipedia.org/wiki/European_Rabbit (http://en.wikipedia.org/wiki/European_Rabbit)
These were introduced by the Normans. Skins from these are usually easily obtainable, and are extremely versatile. The fur may also be blended with other furs, synthetics etc. Depending on what you want the skin for, careful selection may be necessary. The fur varies very considerably. The fur on various breeds of rabbit is subject to massive variation in quality, colour, staple, ( length of fibre) etc.
Domestic white rabbit is often offered dyed as zonker strips, either crosscut or in long strips. The wild rabbit fur has blue/grey ( blue dun) underfur, and is used in very many patterns. Quite a few dressers also use rabbit fur either natural or dyed as dubbing. The guard hair may be used as hackles etc, but it is not waterproof, nor does it have the same resiliency as hare fur, tending to be soft. The natural hides may also be dyed in various colours, which gives some interesting effects, but personally I prefer hare skins for this.
The pieces below have been taken from a wild English rabbit skin back ( left) ,and side ( right). The blue underfur can be seen at the edge of the pieces, and on the side piece it is also clearly visible beneath the guard hair. This underfur is useful for many things, and was considered indispensable by many of the old time dressers. One may use the guard hair for some things, mostly on wet flies.It has a fairly good colour range, but hare fur is superior for most things.
(http://img33.imageshack.us/img33/3779/wildrabbit1.jpg) (http://imageshack.us/photo/my-images/33/wildrabbit1.jpg/)