Justice minister Lord McNally agreed to meet with Kennedy in response to a question in the House of Lords in March.
At the time, McNally accepted the government must do more to crack down on “dodgy practices” used by CMCs and suggested there may be “a better home” for CMC regulation than the MoJ.
This week, Kennedy met with McNally, Justice minister Jonathan Djanogly and consumer group Which?.
Speaking to Money Marketing after the meeting, Kennedy says McNally and Djanogly revealed regulation of CMCs will remain at the MoJ but it is looking at how it can “tighten up” this regulation.
He adds McNally and Djanogly told him they will talk to Treasury financial secretary Mark Hoban about improving the way banks handle compensation claims.
Kennedy says: “It is fine for CMC regulation to stay at the MoJ as long as it is done properly. The MoJ’s thinking about how to improve regulation must be complete before it is too late for consumers.”
An MoJ spokesman says: “We plan to consult on further tightening up the rules used to regulate claim companies.”