The way I see it, the bmi domestics and near Europe short-haul from LHR will mainly stop (especially where there is direct competition with BA today) - the slots freed up will be used for the much talked-about long haul expansion.
Having said that, it'll be interesting to see what happens with LHR to DUB and BHD (which BA don't operate and haven't in their own right for a good few years)
Some of bmi's niche Middle-East/near Asia routes (basically the old BMed business) could be kept, and would enable BA to (once again) place their brand in these markets where it makes financial sense. Of course, they also compete today is some of these areas (Saudi, as an example).
As often happens in M&A situations, it's the HQ-type functions and roles at bmi that must be at greatest risk. For example, BA might be able to "synergise" some/all of bmi's Airbus crews into it's own operations, which could be at the expense of their ab initio Programme.