Registering with private insurer -> company name or individual?

Hi all,
I have recently opened a private MSK physio practice.
From the start, when registering with private insurers they have only allowed us to register as individuals rather than under the practice name - e.g. as Joe Bloggs - Physio instead of Physio Practice Ltd.
As a result, when a potential patient is referred by a consultant to us at 'Physio practice Ltd' , the health insurer (usually axa so far) just says we dont have that company on our database and we lose out on business.

Has anyone else had this issue? Surely practices with multiple members of staff can register under the company name? so far axa and bupa and others have all refused saying its not possible!

Many thanks in advance for any help or advice
D