Our local riding school takes them from 3 but I would say it would depend on how co-ordinated and balanced your child is for that to be effective - as Nemo2007 says, at that age it's just them sitting on top of the horse grinning away at mummy while the helpers do most of the work!
At five your dd should be fine, my niece started at four and by the age of six was fairly accomplished (ie she could ride on her own!) and it's very good exercise.
As regards the snobbery/cliquey angle, there are some places like that, but there are also plenty that aren't - riding in the UK is not just for the monied classes, certainly when it comes to lessons - it's when you move into owning your own (and believe you me, if you go down this road anddd enjoys it you are setting yourself up for 'mu-uum, can I have a pony for my birthday? We can keep it in the garage and it can graze on the lawn, honest!' on a weekly basis!) that you run up against the 'pony club' set.
The best thing to do is find a few places nearby and visit them beforehand to watch a lesson in progress - they shouldn't mind you doing this - and often you can tell over the phone if they're at all up themselves.
If you're anywhere near East London/Essex I can recommend a nicely unstuffy place!
MamaG - sadly this is getting to be the case with a lot of places - because of the "sue 'em at the drop of a hat" culture we seem to be getting from America, many schools are either folding or imposing restrictions like that because of mad insurance premiums.
My local place had to sell one of their horses, a gorgeous Shire who was perfect for the tinies because she was so gentle and good-natured, because they couldn't risk being sued if anyone fell off her because she was so big... v. sad if you ask me - horse-riding is a risk sport, but I think most people who take it up know that and make allowances accordingly.