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Charge rate on UK 13A plug?

This is normal. The meaning of the "10/10A" is that the chargepoint is offering 10A (2nd figure), and out of that the car is currently using 10A (1st figure) - in this case, all of it!

So the 10A is set by the chargepoint, in this case your UMC cable. The UMC in turn decides how much to offer the car depending on which type of plug adapter you have connected, and for the UK 13A plug that is 10A. If you used the blue 16A commando adapter, it would offer the full 16A rating of that plug.

The reason for the lower figure for 13A plugs is a compromise: although originally designed back in the 1940's to deliver 13A, experience has shown that modern 13A plugs/sockets are not robust enough to reliably deliver 13A for hours on end, as they will be used for EV charging.

You will find that just about the only appliance currently sold that takes the full 13A from a 13A plug is a kettle - which of course only runs for a few minutes at a time. If you say "what about my 3-bar electric fire?", I challenge you to find an old-school 3-bar electric fire these days: most commonly sold are 2300W (ie, 10A), and in any case heating appliances are normally only used continuously when it's very cold and so overheating risks are lower.

Even the 10A isn't low enough to guarantee no problems with the overheating of plug/socket contacts if you happen to encounter and old and worn (or new and badly made) socket, but it's usually OK. Note that heating effects are proportional to the square of the current, so although this is only a 23% reduction in current/power compared to 13A, the heating effect is reduced by 40%.
On a similar thread I think this has been raised before but not sure if I have seen an answer.

When go to the charging screen to set a start time and charge limit it only goes up to 16A. This is before I have plugged in the cable so it can’t be getting info from my charge point. However I do only have a 3kW charge point at home. Is it possible that it has remembered that I only have 3kW charging at home and so only gives me the option of up to 16A?
I haven’t yet plugged into a higher capacity type 2 charger to see if it will offer a higher charge limit.
Any one any thoughts? The supplied blue cable seems quite hefty and I am sure would support 32A if not more.
The max on the screen should be the max offered by car/chargepoint/UMC combo. but the actual can be lower and is remembered. So when I finally got a proper chargepoint installed yesterday where I had previously been fighting with shonky electrics, it showed 5A/24A. The new charge point could give me 24A (x three phases - I believe the AC max is 16kW on my car although it shows 17/18 on the screen) but the car remembered I had been running the UMC at 5A before giving up on it tripping the power. So I upped it to the max and am assuming that will now be remembered for next time.
Yes it definitely remembers the actual charge rate but is that also true of the maximum charge rate (second figure - in your case 24A)?

It believe not. That should be decided at the point of handshake between car and whatever you're plugging it into. So when I changed what I plug into but not the location, the max changed but the actual (remembered by location) stayed the same (for the first attempt).
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