Cheapest is not always best as it needs to be sturdy and non slip, also you want it to last some years. You will need some steps down to it from the house and some thought about drainage/runoff? Even if you are thinking of doing it yourself, get at least 3 quotes and see what each one suggest as the best materials to use and how to do it as you can learn a lot and be given ideas you would never have thought of.

As Drc726 says the cheapest will prove to be inefficient in the end. Address the quagmire with a french drain, running any surface water off at the bottom into the lowest part of the garden, to level off will only hold water back. Start with a 3" x 3" meta post with 3" x3" post inserted. Make up a frame with 4" x 2" unfinished timber, treated with a siutable wood paint, cover the area with decking, leave a quarter inch gap between boards. Cover the area with small gauge wire netting, handrails etc. may be needed. The underneath gap could store toys maybe. It's not to cover the whole 7sq. metres, simple steps can be made out of off cuts. Hope this helps, if you shop wisely it will cost up to £400 with a life span of at least 10years, using coach bolts will make assembly easier.

As the most important bits are for the trampoline and swing I would flatten the area where they are to be located.
This would have to be close to the house.
The drainage problem will sort itself out when you have a structure behind this flattened area.
I would use treated timber 4.8 metres long, 8 inches wide, 2 inches thick to make three raised beds, with a path either end and in between.
Your house sounds a bit like my allotment. I have a good 8 foot drop from top to bottom, and the not so good picture will give you an idea of what I am on about.

http://i938.photobucket.com/albums/ad225/oldshobdonion/the%20allotment/allotmentcloches1.jpg

There are other pictures of the beds,

http://s938.photobucket.com/albums/ad225/oldshobdonion/the%20allotment/

but basically they are 4.8m by 1.2m, with 600mm paths between them.
So everything ends up flat with paths and steps going down between them.

What do you have at the sides of the garden?

I would inset a rubber mat at the top and bottom of the slides as that is where the kids will do most damage. I leveled the area where my kids swing is, put over weed supressor then bark chipping. The kids feet eventually kicks away the chips so used some rubber slabs from B&Q (think it was £8 for 2 large ones) and there is now no mess.

If these good suggestions are too expensive a load of sand would probably please the children on fine days.
deal with the drainage problem, and be safer for them to jump about on. Would need topping up every spring.

wow, thanks for the suggestions! I did stupidly neglect to mention that the bottom of the garden slightly levels out a bit, hence why the water all gathers there. The slope goes downwards away from the house. We already have decking at the top, so the trampoline etc would need to be at the bottom, where the swamp is.

Scrumpy, thanks for the photos - it looks a similar size to mine, (it's hard to tell) but I think your slope looks a bit steeper than mine. I'm not sure that I want a few levels, in addition to the decking at the top, but I'll go out and have a look today, to see if 2 levels is doable. Thank you. Oh, and it's just a 6ft wooden fence around the perimeter. Decking next to the house, then the rest is "lawn" - creeping buttercup and swamp weeds, mainly!

Doctorbob1, would I need to add drainage if I am covering it with decking? Thats why I had hoped decking would be a good solution, as we could hide the problem area, rather than tackle it.

Kildermorie and Diane, thanks for the idea - the problem we have is that we have a lot of cats coming into the garden (I've tried loads of repellants, but thats another story), and they have been using an area of bark chips as a litter tray - grrrr. So I fear that adding bark or rubber chips or sand will just add to the problem, unfortunately.

PS I we wont need steps, the area where you walk down the slope, from the decking steps doesnt get as marshy as the rest, for some reason, so it's ok as is.
Drc726, I wont be tackling it myself - just dont have the time or muscle to do it. Hence why I was hoping for a cheap idea before even getting some quotes. I'll start phoning people in a few weeks, with a view of having it done after Xmas etc, so it's ready for next, ahem, "summer".

Does anyone have any idea about costs of labour to have a deck area put in, roughly 2m x 6m? Or to dig out the clay and level off/add drainage to the same size of area?

Yes, you would need drainage, if you leave the swampy area underneath the decking you will be plagued with flies, gnats etc. as well as the smell. I would estimate £1000 plus for the job, but labour charges will vary depending where you live.

Labour will be the main charge. So much for the millions of immigrants reducing labour costs! I am planning a similar project for the kids and the decking was less than £250 and labour for £25 per person for first hour then £15 ph afterwards per person. It seems to take 2-3 days at least to build a deck of reasonable size, normally more.