I retired 7 years ago, so I can't give you a definitive answer for how things are today. Things may have changed. But, throughout my ATC career (Edinburgh, Hurn, Aberdeen, Jersey) we vectored a/c to visual approaches. This could be to final, base leg, or downwind. There was no restriction to doing this except that the visibility & cloud base had to enable the a/c to be able to proceed visually once the radar vectoring had terminated, & there had to be a reasonable assurance that the crew could complete the approach visually to landing. Also, when vectoring a/c to visuals, ATC had to ensure standard IFR separation between a/c. Visual approaches could be carried out to any runway regardless of whether they had ILS or NDB approach procedures associated with them. I don't think much will have changed from the ATC perspective between then & now. However, there have been some high profile accidents which have occurred to a/c carrying out visual approaches due to loss of pilot orientation. This may have had an impact on airline company procedures which preclude a/c of those companies making visual approaches in certain circumstances..