Very strange that you can't get cover. You might need to get an open drive policy, but something to watch out for is if the policy is in company name rather than yours is that you might end up not having an NCB in your own name in future.
Most company open drive policies have s minimum age of 23.
I can't recommend a specific broker, but I'd Google one that does fleet insurance to see if they could help. It's not a fleet policy, but they're likely the same underwriters.
I can get cover and add business use but only with private car insurance which doesn't help me with by BIK ambitions!. I have tried a few of the fleet insurance companies but I think as it is pretty unique its not worth their time or the person on the phone is just not authorised or able to go outside the norm and only interested in 'fleet' work for 3 or more cars.