
Friends of mine have just had this headache, and one of the owners did fly over to get the bitch, and did come via Brussels as it was more cost effective than flying to Heathrow.
They still had to complete a form that it was not a commercial import and that the dog would nto be transferred to new ownership within a specified time frame.
It has to be owner or agent, so |I think the transport company can act as agent.
Anyway there is a link for the form for unaccompanied will see if I can find it again.