pj, that is correct. if you clear security, you are technically entering the UK, which means
you would need to pay for an UK entry permit. It would just allow you to transit through
the UK and do nothing for you entering the EU.
So, don't follow signs to the Tube, or Elizabeth Line, or Heathrow Express. These will
all take you outside the secure area of the airport. Find the buses that pick up in the
secure area of T5 and take you to secure area of T3.
Frank II's article about delaying entering Europe means you might have delays exiting
Nice airport, but since that is your final flight destination, less of a problem.