Yes, I have been gathering the info for you and I apologize for the delay. To answer your question, it is absolutely possible and it requires your dog be microchipped, vaccinated for rabies, dewormed and have flea and tick prevention applied as well as have a health certificate from a licensed veterinarian. It is easiest if he travels with you on the plane as he has to arrive in the UK no more than 5 days before or after you.
The timing of everything (i.e. if your pet will have to be and have another health certificate for return to the US) will depend on how long you are in the UK.
Here is the website I found that has all the information you need to get your dog into the UK: https://www.gov.uk/take-pet-abroad/overview
here is another website that is helpful, this is the USDA website on how to export animals: https://www.aphis.usda.gov/aphis/pet-travel/take-pet-to-foreign-country
It will be helpful to know that HomeAgain microchips can be read by international microchip readers. I do not know of other brands that can. Also as long as the rabies is an approved recombinant (NOT killed) vaccines, it is valid but the dog has to be microchipped BEFORE being vaccinated.
I have also attached an internal certificate that your vet will need to fill out and sign.
As far as returning to the United States, here's what I found. Dogs being imported into the US from other countries have to meet the requirements of the USDA and the state to which they will be traveling. The following is the website detailing all that is necessary to bring the dog back to the state of New York http://www.agriculture.ny.gov/AI/import_export/Companion_Animals.pdf
This is the website from the CDC that details the requirements for dogs being imported into the US http://www.cdc.gov/animalimportation/dogs.html
And finally, the requirements of the UDSA must be met and this is the website for information; https://www.aphis.usda.gov/aphis/pet-travel/bring-pet-into-the-united-states/pet-travel-dogs-into-us
The USDA requirements are the easiest because the UK is free of FMD and screwworm so all you have to worry about is the CDC requirements. These are essentially the same as the UK requirements, thus if the rabies vaccine has not expired while you are in the UK you only have to vaccinate him once- just keep your proof of vaccine and you'll have to get a new health certificate before you leave the UK. To sum up, you basically need to have your dog microchipped with a chip that can be read with an international reader (HomeAgain is the one that I know of that meets this requirement but I an sure there are others), rabies vaccinated with a recombinant vaccine (pay attention to this as some vaccines are modified live and not acceptable for entrance to the UK), be recently dewormed and treated with flea and tick prevention and have health certificate.
All very easy things to do but the timing has to be paid attention to as you have to have the dog vaccinated 21 days or more before entry to the UK.
I hope this information is helpful.
If I can be of further assistance, please let me know. I appreciate your patience, this was a lot of information to gather but I hope you can find it useful in traveling with your dog. If you have specific questions please feel free to let me know and I will do my best to find an answer for you.