Sorry to hear about your daughter's discomfort. The photo isn't really sharp enough to show enough detail, though the spider from what I can see doesn't look like anything out of the ordinary, there are a few possible candidates amongst UK spiders that all roughly fit the profile (stone spiders, sac spiders, maybe even a mouse spider). If it's one of these, the venom won't have any lasting effects, but may well be a little sore for a day or two.
Any chance you might be able to take some close ups? Perhaps in a low walled glass/glass jar (the spider isn't likely to be able to climb out, if it tries just put something over the top, the likely candidates aren't renowned for jumping). Some shots of the head & abdomen (dorsal view) would help.
Taking further pictures has proven difficult but having looked at photos on the web based on your suggested species, I'm pretty sure it was a bark sac spider. The white dots(eyes?) on the head, that look like one as they are close together, and the fact that the spider was walking across the wall in my daughter's bedroom, seem indicative of a bark sac. If I can get better photos I will attach them but in the meantime thank you for your help.