Thanks again for all the replies. Sorry it's taken me a few days to respond.
KJP, I don't think she's missing any important milestones, and moreover I'm sure she could learn any that she's missed if I forced the issue. It was the same with potty training and shoes. I gave her until she turned 3 even though she was obviously ready well before that. When I forced the issue, it was done in an afternoon. With tears, but done.
Chay, thanks for some of the great ideas - pavement chalk, genius! Also glad to hear your DS was still absorbing as you read, maybe I won't give up on story time just yet. I do feel bad that I can't give DD more opportunity to be physical each day, we spend a few hours each day outside but I can't manage much more than that. She deserves a farm but all I can give her are footpaths and slides
DianaG, she's high energy compared to all the kids at the park. She's constantly trying to get other kids (or me) to play tag, or super heroes, or cops, or anything else that involves running. When the other kids are usually playing forts, or sandcastles. She's running. Even climbing doesn't cut it. She needs to run. We usually take a ball along and she runs around and kicks it if she can't get anyone else to play. When she's old enough I'll get her into some kiddy sports classes but there's nothing here (apart from swimming, which she hates) for her age yet.
Puffin, she's nearly 3.5.
RRD, I don't think I will get her assessed. The only reason I would do it (next year, if at all) would be to give her school a heads up before she starts, if she has any special learning needs.
Now that I've done a bit more googling, I think she probably has psychomotor OE (and a few others). I might try to find a book so I can understand it better and equip myself with better techniques to deal with it.
And start looking for a flat near the park so we can spend more time outside, running, each day