Shoey,
again, it depends. Standard sep is 1000ft/5 miles.
In approach control the CAA allow this to reduce to 3m/1000ft
for a tower controller such as myself, in theory separation can be as little as 'as long as they dont hit each other' in the form of 'reduced separation in the vicinity of the aerodrome' which is basically where they can get as close as they want as long as i can see them both/they can see each other and happy to maintain separation.
Below ( i think) 600ft (someone can correct me on this?) tcas RA can be ignored to allow this type of sep.
Also, IFR aircraft can be separated from VFR aircraft simply by giving each a/c 'traffic information' on each other (telling each where the other is) and they can also get as close as they want...