In the UK, airports with AFIS are normally VFR only with no iap's; there are exceptions however if another (IFR) airport can assist with the iap - EGNL is an example - otherwise the pilot should do an iap at another airport so he can carry out a visual approach at the AFIS airport.
As regards the number of aircraft in the circuit, AFIS does not issue 'clearances' thus it is entirely 'pilots discretion'.
There is another service in the UK (Air/Ground Radio abbrieviated to A/G) which provides basic advice such as runway and pressure setting, but AFIS also provides traffic information on other aircraft joining, leaving or transitting the circuit and is also mandated to pass instructions to vehicles and aircraft on the ground.