Your non-UK license remains valid, and is not voided by the issuance of a UK provisional license.
You can drive a small vehicle (motorcycle or car) in the UK for up to 12 months using your non-exchangeable non-UK license. See the presentation on this UK govt webpage.
Whether you can hire a car in the UK using your non-UK license will depend upon the class of license you possess, your age, and the rules set by the hire car firm. You will increase your chances of success by also having a valid International Driving Permit, issued in the same non-UK country that issued your driver's license. (The IDP is not a license, but is an official translation of the terms of a driver's license issued by your country, and is especially useful or required when the driver's license is in a non-English language, or uses a non-Latin system of writing.)