I'm a 48 year old native briton with a 1st class degree and a PhD. I listen to R4 and watch paxman quite often, and read the Times at the weekend.
I got 15 correct. So obviously the test is bollocks.
The questions I got right tended to be the few useful ones like the speed limit. The statistics ones and dates of divorce legalization were utterly stupid and pointless. It really doesn't matter whether there are 2.7 or 3.4% muslims or whatever the numbers were - now, if they'd had figures like 'approximately 1% 3% 10% 25%' it would perhaps have showed whether you had the right ballpark figure on demographics, which is somewhat relevant.
anyway of course you don't need a GPs letter to attend a hospital except in emergency. You just need to have a small child and consult NHS direct don't you?