This is appalling service from UKBA
The Home Office must issue a full CAO rapidly to clearly demonstrate that your application for Residence Card has been made, that they have checked it's validity and that the Residence Card will be processed.
For your side the COA is your proof that you are legally resident without restrictions and with full right to employment just as if you actually had the Residence Card.
If you're experiencing problems registering with a GP or securing employment because of this then you should certainly seek the support of your local MP.
I'm sure an MP's letter to the GP's practice would remove that particular barrier.
Worth a try anyway. Not all GP's practices are fully familiar with immigration rules, and we can't expect them to be so, but by the same token they should not prevent you from registering when a short phone call to UKBA could resolve their doubts.
The same principle would apply to an employer.
The employers and education providers' helpline provides information about the employers checking service for employers who want to verify the entitlement to work for people who are awaiting the outcome of an application made to the Home Office
Phone: 0300 123 4699
Opening Hours:-
Monday to Thursday 09:00 - 17:00 and Friday 09:00 to 16:30 (excluding public holidays)