If you purchased the vehicle from a dealer then you will be classed as an "innocent purchaser" - therefore the vehicle is yours.
You say that the payments have been made regularly over he last 3 yeasr - how do you know that?
It sounds to me like the finance company who have registered an interest in the vehicle have probably put the wrong registration number down.
Phone the finance company up and ask them to take your vehicle off HPI. They may need to see your purchase invoice from the dealer.
If this is not a mistake, then they still need to take it off HPI and deal with the motor dealers.