Unless you've bought the tickets already, or have good reason not to do it this way, I'd recommend not doing this.

The Virgin Atlantic site will sell you the BMI connection as a codeshare - just search for MAN - JFK flights. It will offer you the same combination of flights (arriving LHR at 0915 and departing at 1200), but the difference is that you'll be able to check your bags all the way through, and go through flight connections without having to go landside.

You might also be able to get the same fare from Expedia or a travel agent.