The key to the identification is that is has four small white triangular marks underneath at the base of its middle and hind legs whereas Coccinella septempunctata has only two in the middle. It wasn't easy to photograph but was better with the ladybird in a small glass specimen tube.
The Scarce 7-spot Ladybird goes by the wonderful scientific name of Coccinella magnifica. It is a handsome beetle and was happy for me to take a few more photos.
I also tried to get a photo of the two species side by side but the flash didn't fire as the 7-spot Ladybird (L) walked by the Scarce 7-spot Ladybird (R). The photo was totally underexposed but it is astonishing how Adobe Lightroom can recover this image from the Olympus OM-1 RAW file.
There are still several British ladybirds I haven't found. Hieroglyphic Ladybird is top of my wish list. Do let me know if you know where I can find one - and expect to see a photo here if I do.