You'd be lucky to get to see a GP for 3 days while you're sick in the U.K.
Most of them actually have a new way of booking appointments, and you can see one on the same day you call them. If yours isn't available they will book you in for a consultation with any of the other GPs in the surgery.
This is something that has changed in the last two years.
I agree it would take some modifications to the current system, but it's about time this procedure was revisited.
Alternatively, have a doctor available at BAHS - give us back BAHS at Gatwick. I am sure that all the sickness loss is much more than what BAHS did and would cost.