I’ve had a friend in a similar situation who has had success with Enterprise. This is what their website says in terms of license requirements:
Documentation- all drivers must produce all parts of a valid driving
license. Non-EU license holders are required to have an international
driving permit if the license is not in English. Domestic renters must
produce a photo ID- passport or driving license. International
travelers must produce a passport, proof of return travel and
residency information while in the U.K. renters who wish to use a
debit card are also required to produce two proofs of address such as
a bank or credit card statement, which are less than three months old
and may be subject to additional checks. We reserve the right to
request additional ID or conduct further ID checks. These may include
ID checks with external partners who may check supplied details
against databases to which they have access.
With that being said I would suggest giving them a call before actually booking a car. Their contact details can be found on this page.
If they wind up not working out I would suggest scanning local companies on a website such as Yell. Keep in mind that if you have a license from a different country with an earlier issue date or none at all it’s perfectly legal to show that instead.
Credit:stackoverflow.com‘