Avis and British Airways partner to offer free additional driver to British Airways Executive Club members (BA's frequent flier program).
To benefit from it, you only have to register online (follow the "join Executive Club" link at the bottom of the page). You quote your frequent flier number when booking with Avis and it shall work.
I have booked rental cars regularly via http://www.holidayautos.co.uk (or the German version), which often offer better deals than the rental companies itself. Depending on the actual offer, this may include unlimited mileage, additional driver for free, etc.
Holidayautos.co.uk is just an agency, usually you get a rental car from one of the big companies.
As it has been stated, you may get better deals (which may mean no charge for one or more additional drivers) by booking via a rental car broker (for the US, being based in Switzerland at the time, we had very good experiences with SunnyCar, for example). Brokers have bulk agreements with the rental companies, as well as with the insurance companies, allowing them to provide special packages.
In fact, in one case where we were in an accident (caused by the other one), the only reason the rental car company gave us a replacement car, was because we were on an agreement with the broker.