Hospital and care homea do account for a lot of it. As pp said, I believe, if a patient or worker comes home and passes it to their family, thats classed as a community transmission. But it came from a care setting.
A family member works in an NHS mental health unit. One of the wards is high security as the people on there have commited fairly, horrific crimes but are not well enough to be in prison.
2 patients have recently been diagnosed. Its assumed that they caught it from a staff member who didn't have symptoms. All staff have been tested, 2 had but weren't showing symptoms. It could be the case they caught it off the patient or the member of staff that gave it to the patient, rather being the ones that brought it in.
One of those staff members lives in a shared house with 5 other adults, who are now being tested. Those adults could have it and not have symtpoms, or not started developing them yet and passed it on during shopping, committing etc.
Those 5 adults will be classed at a community infection, potentially so will the other they have infected. But it all started in a care setting.