Doubling it in price but giving away a small number per house per year would seem fair.
Or an increasing cost per permit per household, would “drive” the correct behaviours.
( first 5 cost a pound, 2nd five cost a fiver, next ten cost a 7.5, next 10 cost a tenner, next ten cost 15 and so on ).
Lambeth could actually have made this progressive, eg traders permits assume people using traders are minted - one day costs 23 quid, more expensive than parking meters in most of the borough.