Using the paid left luggage service at T3 Arrivals would be the best option? Then just collect it when you pick up your next flight. I wouldn't think leaving bags on the carousel is a particularly safe move..!
N.B. Not sure how many bags you have, but a quick look on the Left Baggage website suggests it would be £90 for 3 bags for 3 days (
https://www.left-baggage.co.uk)