Hi nines,
There is nothing specific in the EGLL MATS Part 2 regarding conditional line up clearances. We always add the company as well as the type to the clearance to help avoid confusion. If there is more than one aircraft of that company/type in the RHA then we would specify first/second (company/type). I do not advocate third/fourth. Of course we need to be particularly careful about confusion with the plethora of different colour schemes in use by certain airlines or code shares. There is a recommendation (no more than that), that only a maximum of 6 - 8 aircraft are in receipt of conditional clearances. I sometimes add number in traffic to my line up instructions. If there is likely to be any possible misunderstanding of my instructions, or if a particular pilot's English is poor, then I will wait and give line up subject to one aircraft only. Finally if you are at all unsure about the clearance - query it!!