Thanks to everyone for your thoughts.
DD has not been a massive telly watcher or computer user historically, and doesn't have that natural inclination - though she certainly isn't averse to a 'pajama day' where longer sessions occur .
We've recently moved to another country and that combined with the summer lack of structure/routine has, I think, caused her to ask for more time. Also, there is alot on telly she hasn't seen before so suppose the novelty makes it more exciting.
If I'm honest, as a single mum who has had to organise the move and do a great deal of admin now that we're here to set our lives up, I've encouraged her to watch telly/go on the computer when I wanted to be guaranteed some peace and quiet to do something uninterrupted - hence the 'arbitrary' part mentioned in the OP.
Now that we're settling in, and I don't need to be undisturbed so much, I think we/she should cut back - but wondered if I should define that to dd in specific terms, and if so, what is 'reasonable' so she understands how much time she's allowed.
School here (unbelievably) starts on Wednesday of this week, so perhaps I'll simply let the change in routine be the natural limiter instead of big, bad mummy with her rules!