Yes, definitely selected both owner and registered keeper as the lease company.£800 is a pretty good deal, these days. Are you explicitly selecting that the owner and R/K of the vehicle is a lease company? (And not just a company?)
As for Admiral, my wife’s company owns our M3 but she insures it through Admiral as personal insurance but with business use. No issue at all claiming this as a business expense.
I’m waiting for a call back from my accountant and hoping he will say I can claim the Admiral insurance as a business expense. Does this give rise to an additional BIK element?