Tax on Car when transferring the owner?

One thing at a time.

Did your insurers know that the car was in your dad's name? If not then you committed insurance fraud and the policy is invalid and you may lose your money. Better sort that out first and try to explain it was a mistake, or hope that you're still in the 14 day cooling off period when you can cancel without reason.

To transfer the keepers details your dad fills in and sends off the V5c with the new owner details and you'll usually get the reissued V5c in your name in two to three weeks (often quicker). The road tax gets automatically cancelled as soon as DVLA change the V5c. Any refund due (and it isn't pro-rata!) gets sent to your dad.

On the day that you and your dad decide is the changeover day, you need to immediately get the car re-insured. That will be a problem if you're still waiting for the "mistaken" insurance to be sorted out as insurers share databases. The insurer you're cancelling with won't want to do any business with you again as you'll have already wasted their money or they may decide that you've already tried to defraud them. If the latter you'll have trouble getting anyone to insure you at any price as insurers regard liars as an unacceptable business risk. If you do manage to get legitimately re-insured, by not trying to deceive insurers this time, then you can immediately re-tax the car. As DVLA won't refund a part-month and as you have to tax from the first day of the month, DVLA end up getting paid double tax for the changeover month; a nice little earner for HM Gov't.

Unfortunately, in trying to be clever and beat/cheat the system, you've probably just cost yourself a small fortune and may even have made yourself uninsurable.

One other potential problem is the law requiring continuous insurance. If the car was in your dads name then DVLA will check on transfer whether the car was insured in his name or on a SORN. If not on a SORN they may automatically issue him a fine for not being insured. That can give him difficulty when he next needs to buy car insurance...

When you transfer the car registration into your name, the tax will be cancelled, any future payments will cease, and you will have to start again in your name. You will lose the current month, as you will have to pay for this month in your name, but the refund of the tax in your father's name will only be for remaining full months (the AA estimates the DVLA is netting £38million from this "double taxing" of cars on transfer of ownership).