If you look at Stasher (which uses local hotels and stores), for instance, there are half a dozen places within a stones throw of Paddington station.
They charge £4.99 a bag, so 1/3rd the cost. Excess Baggage Co are noted for their excessive charging.
Pre-paying at Excess Baggage Company also does not "skip the line". Paying takes seconds. The line (such as it is and it is even then minimal) is for security checking of your bags.
There are other such internet based left luggage services.
But where on earth are you going to from Paddington that you have a 4 hour wait there. If you are travelling on timed advance tickets and are routing via Paddington on HE then you haven't been well advised on your train ticketing and routeing options.
With that much time in hand you could have travelled to Paddington on the Elizabeth Line for 1/2 the cost and only 15 minutes (or less) longer, if you count the change to tube at Paddington, which would have taken you right into the centre of London (where you would easily have found a stasher or equivalent location.
or have travelled on an off peak flexible ticket on one of the rail routes which avoids London- that way you would have been straight on your way whatever time you are clear of the airport, and it would also have covered for any flight delays (what happens if your flight is over 4 hours late?).
The extra over between Advance Tickets and Off Peak flexible tickets would have almost certainly been less than HE and then left luggage costs and have been arguably more sensible when you are likely to be jet lagged.