So I just asked, and the booking issue is a combination of an IT problem with the website and the capacity being used in the short term. The advice is check again in case anything becomes available. You'd need a taxi to the drive through and the time it takes is indeterminate (I was queuing for quite a while when I did it).

Also check Collinsons drive through which is in Copthorne (use the BA20 code or whatever it is), and Boots at Gatwick which will do a fit to fly but with hugely limited capacity. Depending on where your daughter is going, you might look at the Qured option of supervised test for fit to fly.

Express do day 2, they had a short period where they didn't at the walk in only due to a logistical issue.