Without UK credit and a UK driving record, it's possible to get a car and insurance, but it's expensive. You can get insured with your US license, although the prices are going to be very high. You can also drive on your US license for a year before getting a UK license, but I'd recommend getting a provisional license as soon as you arrive and starting driving lessons soon after. Check out Sainsbury's insurance, because they were the only company that took into consideration that I had been driving for over 10 years in the US. Other insurers will only take into consideration UK driving records, so you'll be a brand new driver, often paying the same as a 17-year-old who has just started driving.
As for getting a lease, it's going to be nearly impossible without a credit history, unfortunately. I didn't have to deal with this in the UK, as I had my husband's credit history to help me, but I just dealt with it moving to Canada where we have zero credit. We tried the "no credit, no problem" dealerships and FINALLY found one that would actually work with us. We have high salaries and were able to prove our finances, so received a 6% loan with a 25% deposit only after proving we were stuck here in a work contract for three years AND getting my husband's HR department to verify the contact. The woman at the bank we dealt with said 30% loans aren't abnormal for people just moving here. So, you MAY be able to find a loan, but the rate is probably going to be very high.
Most people who have just moved countries and have no credit are forced to pay cash for a car. My husband's parents had to do that when they moved back to the UK after 15 years abroad and had no credit history.
We bought a car from Motorpoint, which sells former rentals with "no-haggle" prices and they have dealerships throughout the UK. We got a really good deal and a great car, but I know other people have had terrible experiences with them, so I'd be careful.