Hi Andy
Need more information on the section you mention to bring the dogs to the UK.
Please take a look over in the Pets section for more information, but from what you've just mentioned you won't be allowed to bring the dogs into the UK. There is a 6 months quarantine period I believe. In order to bring the pets over properly, you need to speak with your local vet, who then can start the correct procedure whilst the dogs are in the USA. In effect, the quarantine period is served in the USA under the guidelines of the program. I'm not sure if you can get everything done within a month, and certainly not by turning up in NYC, getting some procedures done and bringing them over.
If things have changed recently, then apologies for getting the above incorrect.
Cheers, DtM! West London & Slough UK!