Used BMI twice, Once via Chicago and the other via Washigton, your internal connecting flight should be with TED, part of United. BMI were advertising more economy leg room than any other transatlantic carrier, I dont know if this is still correct. I would say the first time we flew with them was the best tranatlantic crossing we have ever had. Great inflight entertainment, food was good. No problems at all.
We only fly Virgin for the Direct route and we have about 80,000 miles which gives us some better prices. If I had to pay full rate in school hols doubt I would use them their service has been terrible last couple of years.