First, a word of warning about the bamboo - if you don't intend to keep it in a pot, but want to put it in the ground, unless its Fargesia, you need to insert a root rhizome barrier, or it'll run everywhere, including into the lawn. Bamboos are very useful for screening and privacy, and will grow pretty well in heavy soil, but most tend to take over the ground.

Second - fast growing plants also tend to be plants which don't stop growing, and most will outgrow a small garden within 3 years. Pyracantha can be bought at a good size and isn't a slow grower, so that's a possiblility if you don't mind thorns. Otherwise, knowing which way your garden faces and whether its sheltered or not would be very useful before suggesting other plants.

You joined GOY just in time. You will be astounded with the amount of experience an knowledge these members have of which Bambo is one of the prime examples.

Welcome to Goy
Can I suggest that you look at the alphabet below, click on any letter and a list will come up, then click on which interests you......there are so many catergories , there are photos galore and questions,
Please ask away.....
oh a word of warning Goy is infectious ☺
and check out the blogs too.....

There's a good list of plants for clay on the RHS website https://www.rhs.org.uk/advice/Profile?pid=305 - fairly safe, reliable options. As Bamboo says, the fast growers don't stop growing and they take more effort to keep them under control.
Add trellis to your 5ft fence for extra height and grow light climbers rather than having a solid evergreen hedge.
Take a look at what your neighbours are growing - it will give you a good idea of what is likely to be successful in your garden.

Wow guys thanks, there's some really good advice in there. My garden is facing about 70* north north east. It's pretty sheltered by 6 ft fences around the rear of the house (where the patio area is) and 5 ft fences running along side the lawn to the rea, where tall trees in neighbours garden are. I'm keeping the bamboo in a pot Bamboo...thanks for the warning about planting out, I didnt know that but as the area I want to screen is on the patio, pots are my only option really. I will take a closer look round the site also and check out your suggesstions, thanks :-)

Actually, I've always fancied trying some roses, something that will climb the fences fairly rapidly. Any advise on how to and when to plant them, straight in the clay soil or dig it up a bit and mix it with some kind of fertiliser etc...faster growing types, any help is really appreciated. Thanks so much...i love this site!!! :-D

having seen the photos, it is quite a small area - large shrubs will fill up most of it, so a second option is to fit 1 or 2 feet deep trellis sections on top of the fence on the left, or if its next door's fence, fix 6 foot high rigid trellis panels on fence posts in front, and then use that to grow climbers, in particular, your climbing roses, which must be tied into a support anyway. You'd need to prepare a border or bed along that side by removing the grass in the area you want to plant and giving it a good dig over, incorporating plenty of humus rich material (composted animal manures from the garden centre, something like that, not potting compost though), let it settle while you consider which rose/s you'd like. Many rose plants can be bought bare root ready for supply/planting late October and November, and this is a cheaper way to buy them anyway. If the garden faces north/north east, then likely the left hand top end gets the most sun, so that side is probably best for roses.

You could usefully spend time painting the fences and preparing beds before you plant anything. Planting holes in clay need to be a LOT bigger than the rootball of the plant otherwise water will just collect around the roots and your plants will drown. You should be looking to dig beds about 2 ft deep at least for substantial plants (shrubs etc), you could get away with 1ft deep for bulbs and herbaceous perennials.

I would also avoid straight borders - add a bit of interest with different shapes/curves. Try an Internet search for images of small garden designs for ideas. I found this pic http://lunar.thegamez.net/gardenidea/small-gardening-ideas/small-gardens-ideas-cottage-gardens-berkshire-gardening-design-702x468.jpg - just look at the difference a curved path makes!

You have a real blank canvas - Take a few more 'aerial' photos of your garden and you have a base that you can start drawing over the top of to make a plan.

I mentioned Goypedia before in the alphabet below......click on S then scroll down for small garden ideas and you can look at what other folk do with a small space

Thanks guys...some really good ideas and top tips there. I am not looking forward to digging out 2 ft of heavy clay soil lol, but I know it is the only way. Good idea with the 6 ft trellis; i've actually painted the shed and fence now while the weather is good. I like the curved path pic too, the patio is not on the pic but is almost the same size again, so if I did surround with climbers, shrubs, trees etc i would still have enough space...and that all important privacy. Anyone know the safest distance from my house (or patio?) to plant a tree please? Or do they all vary on root growth etc? Thanks so much :-)

Bit risky to use a tree in a garden that size, the obvious spot is right at the end, but there's already a lot of growth down there. If you do choose a tree or treelike shrub, pick one that doesn't get taller than 3-4 metres, and don't choose a cherry or any kind (they spread out surface roots everywhere eventually), nor a willow (heads for the nearest water source, which might be the sewer or drains) unless its a small one like Salix hakuro-nishiki or Kilmarnock Willow. Amelanchier is a candidate, but choose one of the more recent introductions - these are smaller than A. canadensis, which gets to about 33 feet.

Howabout dwarf fruit trees would they be ok Bamboo?.....its lovely to pick your own apples or plums

Yep - they're certainly less than 3-4 metres.

That's not a bad idea. However, I hit problems digging the border...there is so much rubble on that side that I am only able to dig down a foot. So I have dug out a border along the left side fence and put winter pansies and bulbs and one clematis..?..lol is that even the right name!...will roses be ok in a one foot border do you know? Thanks for the ideas, it's getting there!...

Also i have these tree stumps that a previous tennant must have cut down the trees as they are quite close to the house, so i cant really grow stuff around them. Any thoughts please, i will try to add updated pics!...x

There are chemical root killers on the market but they're not really intended to work on an old stump. So you're probably left with making use of the stumps - they could be used to stand big pots on, or something similar like a bird bath.
If you're feeling clever and have a good electric drill you could hollow out the stumps to make (shallow) bowls for planting.

Ring your local tree surgeons and find out if they have a man with a stump grinder, or know of one, they usually do - get him to come out and grind out the stumps, they usually go down about 18 inches, and ask him to take the debris away. Otherwise, you can hire a stumpgrinder and do it yourself, but its no easy task.