Miller Fisher has lost a contract to the newly formed CFA Solutions, which was set up close to Miller's Maidstone office by several former Miller staff three weeks ago.
Diamond Claims Service, which does claims handling for Admiral, transferred its account to CFA shortly afterwards.
CFA boss Colin Farley said Admiral was not the only one of Miller's clients to transfer to CFA, but would not name any others.
“If clients want to follow us because they've got a longstanding relationship with us and confidence in us, that's up to them,” Farley said.
An Admiral spokeswoman said the company had followed Farley through his various ventures since 1994.
She said Miller, and now CFA, handled a lot of work for Admiral.
Miller Fisher would not comment on the issue.