You'd need to comply with US and UK wildlife laws and this is costly.
You will need to apply for and obtain a CITES permit ($100USD). This is currently taking 2 months for permit to be issued. Make sure you fill out one for 'pets', and not the commercial form.
You will need to book an inspection by a federal wildlife agent, and this runs up to $331USD for a CITES II (ie ball pythons) export ($95 less if done at a designated port).
You will need to fill out a 3-177 declartion form (this price is included in the $331).
If the inspection is done at a Non-Designated port then an 'Exception to Designated Port Permit' will more than likely be required. (Contact your US Fish and Wildlife office for details). I know for commercial exports it's definitely needed (which is what we service), but not sure if it's required for exporting pets.
For export of pets, a US Fish and Wildlife Import/Export license generally isn't required. I would confirm with that office again though. It all depends on which agent inspects your shipment..
On the UK side you will require a CITES import permit, as well as providing health certificates that you got from the U.S., and more than likely vet clearance fees once animals are in the UK, import clearance fees etc. The original U.S. CITES export permit and 3-177 declaration (both stamped 'CLEARED') form must accompany the shipment.
Price can easily reach $1500USD with paperwork, inspections and freight charges.
Hope this helps,
-Sam Fard