You are allowed to use your old driving license for 1 year after entering the United Kingdom. This also means you can drive as a learner without L plates until your old license is valid and go to the test centre using your own car with no one accompanying you. You will need to fit your car with L plates for the duration of the test though, and make sure it is insured properly for you to drive it.
However you are only allowed to use a hire car if it's fitted with dual controls: https://www.gov.uk/driving-test/using-your-own-car
Hire cars
You can take your test in a hire car if it’s fitted with dual controls and meets all the other rules.
There are definitely companies specializing in renting dual control cars, however they might refuse to rent if you are alone and not accompanied by someone having a full UK license:
You must be 17 years old or over, possess a clean, current UK provisional licence and be accompanied at all times by a qualified driver, who is 23 years old or over.
Generally you don't need anyone else to be present during the test, as it will be only between you and the examiner. (This is true even if you don't have a valid, but not-exchangeable license)
This DVSA examiner claims your case happens fairly often
DVSA Examiner (Verified by admin)
See it plenty of times - international licence holder rocks up to the test centre, puts on L plates, fails (or passes), removes L plates and drives away themselves again.
It's a rather strange loophole - if they've failed the driving test they're potentially not safe to be on the roads yet can drive away as if nothing has happened.