Whilst I am travelling, I would like to rent a car from NY or LA. Is it possible with a UK provisional driving licence?
Almost certainly not. Firstly, the U.K. provisional license is not a valid full license to drive alone in the U.K, much less the United States. Provisional license holders must be accompanied by a driver with 3 years experience, a full license, and be aged over 21.
Secondly, whilst the U.S does not require U.K. citizens to have an International Driving Permit to drive there, it is strongly recommended for insurance purposes. The IDP requires a full driving license, or a test pass certificate + your provisional license.
Whilst this suggests you might be able to get away just using your provisional hoping no-one notices, you're renting, not borrowing a car from a friend, and rental terms are generally more stringent than the law - for example, Budget generally requires an IDP.
Thirdly, insurance typically requires a full driver's license. Those on provisionals / learner permits are usually covered by the supervising driver's insurance.
Speculatively, I imagine the large enterprise rental firms will see U.K. licenses all the time, and the fact that the provisional license is clearly marked as such and has a large red 'L' on it means they will quickly establish that it's not a full license, and as such not valid.
I realise this is a combination of half-answers and common sense, and of course contacting a hire firm in the U.S. is the only way to 100% verify, but the fact that none of the FAQs / Help sections I looked at even mention the possibility of using a learner / provisional license suggests to me that it's out of the question (as opposed to totally acceptable and as such not worth an FAQ).