Because Cameron was next to a patient, possibly shaking hands, and may then have gone to another patient (after washing hands). You can't wash your sleeves between seeing different patients.
What exactly are the rules then? Because visitors don't seem to have to have short sleeves. There's also a chap sitting in the corner in the clip with a long green jumper on (think it was green).
They still haven't stopped showing this, and David Cameron wasn't asked to leave at all, since he'd taken his jacket and tie off, and tolled his sleeves up etc. I'm not sure what the doctor was on about - doctors and nurse have to be sleeveless as they're going up to one patient, then another...