www.gov.uk/guidance/rapid-lateral-flow-testing-for-households-and-bubbles-of-school-pupils-and-staff
Looks like it should be possible for nannies to obtain test kits in bulk for use at home soon, or to have them via post.
County councils are also running local testing centres but in my experience so far they are not open hours that many nannies can attend (I'm in Surrey and my local centres are not open before 8am or after 6pm).