This is just for reference, in case it helps some future traveler.
Yesterday I entered the UK through Calais using the emergency second passport issued by the Embassy in London. I didn't have my old passport that contains my ILR (that's with UKVI, along with my normal passport). I did have to show photocopies of my old passport , and the letter from UKVI saying I was applying for a BRP.
What this means is that if your situation is similar to mine and you have to send off your passport for 6 months to get a BRP, you can still travel as much as you like during those 6 months by getting a second passport from the Embassy.
Good Luck!