If you were booked on a BD flight with a BD flight number (not a codeshare) and you have now been moved against your will (due to the cancellation of the BMI flights) to VS, then BMI will give you the miles. This has been confirmed by the BMI lurker on FT.

You can easily double-dip by crediting the same leg to a VS account. However, for safety, you may want to remove your Flying Club number from the booking before taking that leg, so BD doesn't see it when you claim your miles from them. You can then retroactively claim your miles from VS.

Note that there is no point in crediting all your VS legs to BMI, as N class Virgin flights credited to BD earn NO miles if they are for transatlantic flights, according to my little guide. You COULD credit your LHR-BOM VS leg to BMI, earning 1.5 x miles. This would probably get to the 18,750 miles you need in BMI for a one-way UK - Europe redemption in business.