Note that the UMC Schuko adaptor is good for 13a, the UK plug is only good for 10a (It's 13a, but only 10a sustained). 10a will always be the limited with an EU-UK adaptor, because that's the limit on the UK side.
I've bought a 16a Commando adaptor for the UMC, and have had toughleads make me a version of their modular EV cable with a Schuko, UK and 16a commando plugs, and a female connector for the 16a UMC. I've then got to adjust the car to pull the appropriate current for that I'm doing. Means I can pull 10a from a UK plug, 13a from a European, and 16a for a Commando. Some of the cable is 2.5mm2 rather than 1.5mm2, which buys me use of the 16a over longer lengths. The Modular EV connectors are good for 16a, so that's the limit...
It's best to avoid cheap EU to UK adaptors. Best case you're limited to 10a, worst case, it's cheap materials which won't do 10a sustained, and melts.
To reiterate previous advice, cheap generic extension leads are rarely designed for 10a continuous. You want *at least* 1.25mm2, if not 1.5mm2. Most are 1mm2. Always, always, always unspool the cable from any reel.
Unless you know the electrics are good, turn off the car charger while you're doing other power consuming things, such as kettles, electric overs, electric showers, etc. Popping the breaking and making the owner faf around fixing it is a sure way to make sure the next person is told they can't charge.