The U.K. government was barely able to test 10,000 people a day at the end of March. A lot more people had COVID in March/April than were showing up in the official numbers. It's only since early May that the circa 150K tests per day U.K. testing capacity is large enough to (probably) ensure that there's an accurate picture of infection rate.
People receiving positive antibody test results don't get counted in the numbers you're referring too. Also, the science indicates that people can fight off COVID using T-Cells and won't necessarily have a meaningful immune response which will be picked up by antibody tests.