From the HP studios website FAQ-
Do you have a cloakroom? Yes! Coats, bags and suitcases can be left in our cloakroom free of charge for the duration of your visit. Please note that we are unable to store food in our cloakroom.
Nannybag use the Premier News Food and Wine Supermarket, 5 minutes walk from Watford Junction station, so more convenient than the Premier Inn.
Presumably you intend to use either the #724 bus or the Rail/Air Bus to Heathrow afterwards- which have almost identical journey times (50 to 55 minutes). The Rail/Air is a coach-bus whereas the Green Line 724 is a city bus, and a quarter of the price. Between the two routes it's a half hourly service.