Microchip is the first thing. If that's already done, then it's the rabies vaccination. If you are current, you could go to the next step, which is blood draw and samples sent to the FAVN lab in Kansas. From the date of the blood draw (with successful results) you have to wait 6 months before your pets can travel
If none of these things have been done, the microchip can be inserted and the rabies vaccination given in the same day. Just make sure the chip is first and the number recorded on the vax paperwork. Then you have a little time to figure out how the rest of it works.
You have plenty of time to make it by September, but if you don't have the chip and vax, you need to get on that ASAP.
If you are prechip stage, you could make your life easier by getting an international chip. It's not essentail to get into the UK, but to keep your pets maintained on the program so they can go back - it helps.
I didn't do the transport company, so can provide no info there.

oh and it cost me $1600 in transport fees on BA, taking 3 cats from Atlanta to Gatwick in Sept 08.