I think you are getting confused over the difference between registered "keeper" and registered "owner" . They are not always the same thing, especially when there is any sort of finance agreement which concerns the vehicle, It comes down to the legal definition of owner - the lease company legally own the vehicle but lease it to you for a monthly payment, you are the registered keeper (the person to whom the police will come if there are any offences which concern that vehicle).
They will be the registered OWNER as legally they have title to the vehicle - you can't sell it, for example. (if it were HP then the finance Co. own the car until you have paid for it, then you do).
You, however, ARE the registered keeper if the car is KEPT by you at your address and used by you. However, if you were to write it off then the insurance company would pay out to the registered owner - the lease company, not you.
My company are the registered OWNER of my company car, but I am the registered KEEPER for the insurance.
This is a very common misunderstanding, but all insurance companies understand it - it's either you or your lease company that is confused!.