I've got a nice bag from Mia Tui which is fab - all their bags are waterproof inside and out, have at least one neoprene bottle/umbrella holder on the inside, come with 2 or more little wallets, one clear, one same as the bag to put things in (nappy kit, medicines, dummies, snacks, etc) and you can buy more, lots of different pockets on the inside including one that is phone sized and some pen holders, and an elastic strap with key clip on the end so you can safely attach your keys. The insides are also bright pink or turquoise so you can see stuff in them - things always get lost in dark bags I find!
I use the Grace bag with just one strap so it is about elbow height which I love, although if you add an extra strap it can get longer if you like it like that. I am lucky that I got mine last year, it's a pewter colour and I have had loads of compliments for it. But they seem to have lots of colours...
I am out of the baby stage so it is maybe a bit smaller than you would want as a baby handbag But it's big enough for me to have a drink, purse, camera, cardigan, iPad, notebook, pouch with first aid emergency kit and make up, pouch with pens and paper and toy cars for 2 small dc, snacks for me the dc, phone, about a month's worth of receipts and general gubbins that builds up when you are not looking... They have lots of other styles too though and have won awards from baby magazines etc for being great baby bags and from other places for being great bags. They often seem to have offers on facebook or twitter for money off so although it costs £45 you'd get it down to about £40 (or maybe MNHQ could talk to them and see if they could organise a discount for when they do their mumsnet offers mailing?) (Just checked their facebook page and they have 20% off a grace bag plus you get a free small bag to go with it too.
I don't have anything to do with the company - just have got one of their bags and I luffs it very much 
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