Ah, immaculate timing for this question, since I had a Verona - LGW - EDI last week, with a 60 minute connection, and I was curious about how well it would go.

I therefore used the trusted stop watch on this. However, two caveats, I was incredibly lucky with this connection, since it was the same aircraft and same crew on both services (indeed I had flown - by coincidence - with the same purser for 4 consecutive days on 5 unrelated flights, to considerable bemusement all round). My other stroke of luck was that I arrived into gate 53 and obviously departed from there. Apart from being one of the few gates which can handle both domestic and international services, it is also extremely near both passports/arrivals and departures/security. Therefore you need to factor in extra, this is the very best possible connection time

So arrival at stand, seatbelt sign off: 00:00
Doors open and leaving aircraft: 01:53 (1 minute 53 seconds)
Arrival UK Border: 06:22
Complete UK Border: 09:32
Arrive landside (always bear left after passports): 10:28
Arrive Premium Gatwick security (actually one channel on main security): 11:20
Complete security check: 15:17 (included a random frisk)
Arrive BA First lounge: 17:08

So as you see even on a one hour connection I had a good 20 minutes in theory in the lounge, but in reality the Verona aircraft arrived 10 minutes early, so I had some more time than that. You can leave the lounge 25 minutes before departure time for domestic.

To get from arrivals landside to Premium Gatwick, use the lifts in front to Level 2, note most people get out at Level 1, then head down the D aisle to main security, if the left most entry point is not open for Premium Gatwick head towards the B aisle for the usual entrance area.

I do not think collecting luggage is viable, but as already mentioned I don't think this is an issue - just get it through checked. Strangely it may help in this case, in that you can minimise your hand luggage and therefore shorten security and be more agile.