Yes (sometimes), said the EAT in Whittlestone v BJP Home Support Ltd.
W was a care worker. She was paid £6.35 per hour for time spent attending to clients at their homes, but nothing for travel time. She also undertook "sleepovers", when she was required to be present at a client's home from 11pm to 7am, and for which she was paid £40. She was provided with a bed, and permitted to sleep except when her services were actually required. It was common ground that she was doing "time work" for the purposes of regulation 3 of the NMW Regulations 1999.
W was entitled to the NMW throughout the time she was required to be present, irrespective of whether she performed any tasks. She was also entitled to the NMW for her travel time between clients' homes.