W have quite clear requirements in our AIP for a Visual Approach, and until they are achieved and the crew advises ATC that they are "Visual" ie they can comply with those requirements, then ATC cannot issue a visual approach clearance.
If cleared for a visual approach, you comply with the STAR (if you are on one) or you track to 5nm from the airport then position for a circuit/pattern or as otherwise directed eg "direct to left base". You must still get a separate clearance to land from the tower. The is no "minima" per se.