After speaking with NHS 111 it looks like my daughter does indeed have coronavirus. The doctor said that it tends to go one of two ways: getting pneumonia as the secondary condition or bacterial tonsillitis. Because she's got an incredibly sore throat it looks like she's, fortunately, got the latter. It's still not pleasant but it's not the direction that results in being hospitalised.
We've got to go to a pharmacy tomorrow but then isolate for 14 days.
The chances are that the rest of the household already has it and is asymptomatic or hasn't started showing any symptoms. Let's hope it stays that way.