When you check in at LHR you will be checked into both flights, so you will get 2 sets of boarding passes and your luggage will be tagged for its final destination, so no worries there.
When you get to Milan, you go through the passport control, everyone queues like sheep but you will see some passport copntrol desks with no queues, where you can show your passport and walk through, no need to queue, we are EU!!

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Next advice, after finding out where your next boarding gate will be, check the time for boarding, then head for a spot of shopping in the Nike shop and other shops..
Have a good journey, if they hadn't bumped me at LHR the only bad thing I would have to complain about is the food, as the stewards were good, the flight was excellent and there was plenty of leg room. Just no entertainment, but the flights aren't long in any case.
Hope this helps.