Make sure your vet who is doing the rabies titer blood draw is certified by your USDA veterinary office -- their name should be on the USDA list -- I think this part requires that your vet be on their list though not necessarily the other parts of the process.
Make sure the chip is put in before the rabies shot, and that the titer blood draw is (naturally) done after both of these. So the order must be: chip, rabies vac or booster, blood draw. Equally important is to ensure that some written record is made to confirm that one came before the other; if the UK authorities looking at your paperwork can't see clearly that the correct order was followed, it's going to be a problem. They've got to see that the chip came first basically, so that they know this was the "same animal" all the way through the process.
The Defra website is not updated very well, but if you actually give them a call, you get to speak to usually a live person ultimately, and they can clear up any doubts, queries or potential mistakes. The person I spoke to was great and tolerated a very long series of questions and double-checking of my facts that I needed to do to be sure I wasn't messing up.
As long as all rabise booster shots are up to date, the titer blood draw can be done the same day as that newest shot -- but if your previous shots have lapsed for any reason, the antibodies may not be up to a good level already, and if this is so, that day's new booster will need time to work it's magic and raise your cats' antibodies to a level that will pass the titer. In this case, you may have to wait a couple of weeks to let the levels rise --- I was advised to do this...after which, when the results eventually came back, my cat passed with sky high levels plenty beyond the "pass" level. But usually, yes, if all shot are up to date already, you can do the "new" one and the blooddraw right after it, same day. You need the FAVN document for your vet to fill out and send with the blood sample to the Kansas State University, the only lab in the US acceptable to the UK for the results.
Just be sure that chip is the very first thing, and is recorded as being so.