Would presumably mean those who came on work or student visas, brought their spouse and children, then applied for asylum once those visas had expired. Would also mean families who were given holiday visas to visit the UK, or who didn't need a visa, but failed to leave after the holiday, stayed and applied for asylum.
Will also include the small numbers who arrive with children via the channel or people smuggling routes.
Some figures here, though it doesn't split the stats between individuals and families.
https://www.gov.uk/government/news/visa-brake-imposed-on-4-countries-after-widespread-visa-abuse