Swinton has had to write to 650,000 people who may have been affected, offering them a full refund. So far 34,000 have replied asking for the money and received an average of £55 each.
However, to get hold of the compensation, customers need to have replied to the Swinton letter and made a claim.
The financial watchdog, the FCA, says customers who think they may have been mis-sold should make a complaint to Swinton, whether or not they can remember receiving a letter.
Swinton has set aside £11.2m for the payouts. If all the 650,000 claimed successfully, the bill would climb to around £35m, based on the average payment so far of £55.
The FCA has fined Swinton over £7m. It says the company used aggressive sales tactics over the the telephone to persuade people to buy add-ons to their car and home policies.
Those extras included breakdown cover, emergency assistance in the home and personal injury cover, sold from 2010 to 2012.
In some cases Swinton did not even tell customers that the add-ons were optional, according to the FCA.
Swinton is Britain's largest High Street insurance broker, with 500 branches and 3,000 staff. It is part of a French mutual insurance group called Covea.