Thanks for the replies.
The in-bound TPA-LGW only allows 2 hours to connect to the LGW-ALC flight, which I don't think is sufficient, given that I will need to clear immigration, collect my luggage, check-in again, pass through security etc.
It certainly won't make for a stress free flight, worrying about making the connection.
My option will be to book 6 hours at the Yotel, have a nap and a shower, and then catch the afternoon EZY flight.