She did not appear to have broken legs, but she was in pain when the vet lifted her. The vet said she may have broken her pelvis, but he was not worried about this, he wanted to wait until she was calmer and was going to X-Ray her to check for internal injuries.
We left her at the vet who gave her a strong pain killer and she had already started to settle down within 30 minutes of being hit (the vet came out when we rang on New Year's Day and arrived before we got there so she couldn't have been treated quicker if we tried). The vet said he'll phone us in a couple of days, so we'll update this post when we know more (as we live in Colchester).