The blood test is for rabies antibodies. Since the UK is a rabies-free island, they take the rabies thing pretty seriously and won't allow any animal to enter that could be at risk of bringing the disease with them.
The required process is to first microchip your dog, then to vaccinate it against rabies, then to test whether the dog has produced sufficient antibodies against that disease to be protected against getting it. If your dog has failed the blood test, it means it has produced insufficient antibodies to be considered protected against rabies.
Now the reason your vet is suggesting taking another blood sample is probably because it can take a little time for the antibodies to be produced in sufficient numbers to reach the level the UK government requires. So if it was only a month between the vaccination and taking the blood sample, it is possible that she has now produced a greater (and sufficient) number of antibodies... So worth a second try.
How much time do you have though? If you've got a spare month, I'd suggest giving her a second rabies vaccination right away and then taking another blood sample in a month's time. I know that's a lot of vaccinations, but you just take another sample now and she still fails, then you're in the position of either having to give her another shot/blood test or else just not taking her.
I recall that the first time I wanted to take some dogs from the UK to Europe (same procedures apply, since the dogs have to return to the UK) and I had plenty time available, my vet suggested two rabies vaccinations a couple of months apart before taking the blood sample. His reasoning was that since some percentage (can't recall what) of animals wouldn't produce sufficient antibodies after only one vaccination, it was wiser to simply give them two rounds before proceeding with the blood testing. It worked - they all passed. Quite likely they would have anyway, but the point of that story was just to let you know that there is a percentage of animals (of which your girl is obviously one) that don't produce enough antibodies to be protected after only one vaccination and a second shot is generally the answer to that.
Good luck, and do let us know how things go.
