The answer is probably 'Yes'.
Laws on minimum pay don't apply to being 'on call' while away from your work site. Your situation (where you're 'on call' but at your work site) seems to be a bit of a 'grey area' but many of the other regulations about employment rights don't apply in full (if at all) to jobs which require continuous staffing (such as care homes).
Your best source of information will be the ACAS helpline. See under 'Where to get help', here:
http://www.direct.gov.uk/en/Employment/Employe es/WorkingHoursAndTimeOff/DG_10028519
Chris