It is not clear from your question whether a claim for a total loss was made following the vehicle being �trashed�. If a total loss payout was made the policy is cancelled and no refund is due (even if it just one day old).
If this happened your friend would have needed to take out a new policy to continue driving any vehicle.
As Loosehead has said, an appeal against conviction cannot be made following a guity plea. Your friend can ask to have the case reopened and change his plea, but magistrates will need to be sure that something significant has changed since the original conviction. He can appeal against the sentence imposed, but as six points is the minimum magistrates have to award for no insurance success is unlikely.
If he pleaded not guilty to no insurance but was found guilty following a trial he can appeal against his conviction and/or sentence but this must be done within 21 days of the trial.