I dont think there's too much to gain by knowing the complete numbers of those with the virus.
After all, if you're diagnosed, invariably you're sent home to self isolate for 2 weeks. Same instructions if you've come back from a high risk area. After that period you're free to resume your normal life. If you're more vulnerable and have more serious symptoms then go to hospital and get looked after.
Individuals need to listen to the advice and self isolate if they show signs of symptoms. If the nhs concentrates on testing, just to draw a graph each day, it pulls resources from treating those most seriously affected.