Cameron said the ruling essentially says High Court Justice David Gendall was right to allow a representative action, which would be a just and efficient means of dealing with the claims.
The Court of Appeal also envisages that Southern Response, set up by AMI to deal with earthquake claims, tell other potential claimants about the proceedings.
"We think the new Government will probably take a great interest in now getting the matter moving forward so, yes we expect action," Cameron added.
Read more: Financial aftershocks continue for quake-hit families
Southern Response said in July it believed a group action would delay the settlement of individual claims.