The full council is a meeting of councillors, and so nobody who is not a councillor is automatically involved. There is no half way house. Someone can be co-opted through the usual procedures if there is a vacancy and no election has been called, but then they become a councillor.
However, to the best of my knowledge, a council is free to decide for itself what rules to apply concerning representations by members of the public, and settle the rules in its standing orders. A larger council or a principal authority is likely to have quite restrictive rules. Smaller councils may choose to be more flexible. The council of which I am a member has standing orders that allow the chairman to permit contributions from the public at any point, subject to the chairman's discretion.
This obviates the problem that if the council meeting is suspended to allow a member of the public to speak, then it is not clear that there any rules of procedure in force. Putting more flexibility into the standing orders means that the meeting continues to be governed by the standing orders, the chairman remains in control, and members can (for instance) put a motion to move on to the next business.
Of course, allowing discretion to the chairman can be harmful if the chairman acts irresponsibly.
