Yes. Most car rental providers will permit you to add an additional driver to your booking. However, an extra fee may apply for any additional drivers. They will need to present their licence at the counter in order to be added to the rental agreement.
Few car rental companies consider the renter's immediate family as authorized drivers. Note also that additional drivers must meet all rental requirements and be present to sign the rental agreement.
Read more about picking up a rental car in the UK.
