The scooter had no front number-plate. They were still compulsory in 1959.
Cynthia responds "You were homeless?" in surprise when she hears that Mrs. Lacey used to sleep on the streets with her baby. In the 1950s Britain, the term "homeless" typically had a different meaning and was not the equivalent of sleeping on the streets. Homeless people were typically transient individuals who had no family connections or social support, or sometimes families living in welfare homes. These homeless often relied on charities or institutions, but they were not necessarily unhoused. A better term for this era would have been the slang "sleeping rough," which is still used today in the UK.