The FAA's "Precision Runway Monitor" (PRM) radar system permits independant parallel IFR approaches to runways spaced less than 4300 feet apart. There is currently, no such operation in the UK (the only locations where it would useful are Heathrow and Manchester but there are planning & environmental constraints precluding this at the latter, anyway).
At Heathrow, whilst parallel landings are undertaken on easterlies and 'Tactically Enhanced Arrival Mode' for 27L/27R, the spacings in IMC are staggered to provide the requisite radar separation i.e. the approaches are not "independant".
Don't know about custom-and-practice in mainland Europe.
PRM is also used at Sydney.
Vortex wake separation becomes an issue if the runways are spaced less than 760 metres apart.
Checkout:
www.faa.gov/AVR/AFS/PRMtraining/index.cfm, http://www.tc.faa.gov/acb300/techrep...4_MPAP_sum.pdf and
www.airservices.gov.au/pilotcentre/projects/prm.
