There are plenty of contractors, some with quite capable types such as the Mi17 and Mi26.
However, the skill sets of the crews (for instance, would they be able to coordinate with UK forces properly as they approached a 'hot DZ'?) and defensive aids standards would all be issues here.
If we needed helos for a 'rear area' then they could probably do a credible job. But there are no such places in either Iraq or Afghanistan right now.