The BMI policy is strictly no through-check of luggage with separate tickets.
However as check-in in handled by Lufthansa at HAJ, your chances are a lot better.
Technically it is possible to interline the luggage (the check-in staff can enter the information printed on the baggage tag manually) and 90 mins should be a valid connection at LHR, so smile and ask nicely.
If they can through-check your luggage you only need to visit a transfer desk in the Flight Connection Centre at T1 to pick up a boarding pass.