ol smokey has a very good question - what do you already have? And the next question is, what do you want to do? Are you car camping, are you going to walk a couple of miles, etc? And when? Summer means lighter kit, etc.
We've just come back from North Scotland with our eight and eleven year old kids, and there was a lot of moaning about walking. To be fair, a lot of the ground was quite boggy, and it rained a lot, but a couple of miles each way (especially up hill) was seen as a lot by them. So be realistic - its not a selection for the SAS, its a trip out with Dad.
For their kit (fleeces, trousers, waterproofs), cheapish Go Outdoors, Millets, Blacks, etc was fine, apart from boots, which we got for my daughter from Cotswolds. Around £45, but they have to fit and they have to work (the Cotswold Explorer card can either get you money off, or at least a freebie). For my eight year old son, boots are much thinner on the ground, which is part of the reason he was less inclinded to want to walk all that far in trainers.
As far as your kit is concerned, the biggest and heaviest things are sleeping bags, sleeping mats and tents. If you paying £40 for a sleeping bag, its going to be pretty big or pretty cold. The saying 'you can have it cheap, you can have it light, and you can have it good - chose any two' is very apt. If you can stretch to down, then Alpkit is your best bet, or for synthetic, Mountain Hardware does a highly rated range of their Lamina series, which are not much heavier than down. Alpkit has a good comparison list on their website about sleeping mats, and their mats are back. Tents? The heavier, the cheaper, but a three man tent is just about OK for an adult and two kids, but its going to be tightish. Millets keep emailing me about offers, but if your lightening up, its going to cost you. I chose a Zephyros 2 over a Banashee, because the weight was so much less, for not much more money.
Best advice I can give is to write out what you want to do, how far your going to walk, etc, plus a kit list of what you (and they) already have. You can't do much about their sleeping bags - they are going to be cheapish and big (the £35 bag we bought for my daughter a while back is huge), but they can probably carry those (although find a decent pack that fits them is going to be a bit of a pain - normal schoolish rucksacks are your best bet, but your not going to get a sleeping bag in them). And dont take the ones with a velcro fixing on the straps - OK to avoid them strangling each other at school, but they will pop in the middle of nowhere and then you've had it. Decent socks, waterproofs, etc will all help. Alpkits drybags are excellent value.
The Cotswold catalogue is very useful (you will get it free if you get one of their explorer cards) - because you get to see what stuff weighs, costs, etc. Much easier than going from website to website. And look at Outdoor Magic - this kind of question comes up regularly.
Ultimately though, they are kids, which means they can't walk that far, and dont want to get too cold or soaked. Personally, I'd car camp, plus a bit of walking. If you want to lighten up your kit, thats great, but I suspect by the time you've bought some of their stuff, you wont have much cash left!
