+1. In their mind, your visa issues are none of their business and they will not suspend their rules to avoid your need to get a visa any more than they would suspend their rules to make it possible for you to take a flight which you would miss by needing to pick up your luggage and recheck it.

Incidentally, since their contract with you is to DME and you would need a visa to enter there, expect them to give you trouble if you try to board without a visa, so even if you do hand luggage to be able to transit, go to LHR very early with printouts of onward travel and expect to need to argue for them to let you fly without a visa.