In my travel from Italy to US I have a 2 hours layover in London Heathrow.
I've not travelled since brexit, so I'm wondering: do I have to re-checkin the baggages or do any time-consuming task or I will just walk to the other terminal to catch the connecting flight?
Since both flights are on the same ticket (and airline), no, you shouldn't have anything special in Heathrow:
At you point of origin, bags will be "through-checked" to their final destination. You should see on the luggage tags both the intermediate airport (LHR) and the final airport. You won't see them again until your final destination (unless you have another connection in the US). No need to wait for them, go through customs, check them back in.
You should get boarding passes for both flights. In some cases they won't be able to issue the boarding pass for the second flight, in that case you'll need to approach a transfer desk when you arrive in LHR to get your subsequent boarding pass.
When you arrive in Heathrow, just follow the (purple) signs for connections, use the bus to change terminal if needed, go through security, look up your flight on departure boards, and go to your gate. If you are on time chances are it will not be shown yet, you'll just have to wait for it to show up in that case.
You will not be going through passport control either.
BA uses mostly terminal 5 in LHR, but some flights arrive in Terminal 3. If your incoming flight arrives in Terminal 3, you have to take a bus to get from one terminal to the other. Make sure you follow the purple Flight connections signs to get to that bus (which is "airside"), do not follow Exit/Passport Control/Baggage Claim signs.
Terminal 5 has several buildings connected via an underground people mover, you may have to use that depending on your arrival and departure gates.
