Hi there.

What type of soil do you have?

What is the aspect of the fence (north, south, east, west)?

Is the fence in sun or shade?

How much space do you have (conifers can be very wide-spreading or very narrow)?

Remember that a fast growing conifer won't stop at 12 feet and will need annual topping.

I'd go for Cotoneaster. Fairly fast growing plus berries for the birds. The variety I grow goes up till it reaches about 10 feet or so and then starts to spread out as well, so you get a lovely broad canopy. It can lose its leaves in a very cold winter, but will recover. Cotoneaster exburiensis. One of my stalwarts for screening.

Hi Rosierose, Steragram and Cottagekaren,
The fence faces east but is shaded by a shed at right angles, therefore gets very little sun. The soil is heavy clay.
There is about 6ft of space in front of the fence and plenty to one side but only a few feet the other side because of the shed. As I write this I am beginning to wonder whether a conifer is the best idea??!! I know a common laurel would grow quickly but I'd like something a bit more interesting.
I really want the top wide enough to screen the buildings which overlook my garden. I hear what you say, Steragram and certainly topping the tree would be an expense I could do without but unless it needs it within 15-20 years I doubt I'll care! I will look up your cotoneaster Karen, but would it make a thick enough screen? I planted 2 rowans outside the fence but the foliage is very sparse, although very pretty and the birds love the berries.

Blue Arborvitae (Platycladus orientalis 'Blue Cone')
Wilson Holly (Ilex x altaclarensis 'Wilsonii')
Hillspire Juniper (Juniperus virginiana 'Hillspire')
Spartan Juniper (Juniperus chinensis 'Spartan')
Newer hybrid hollies: 'Conaf' and 'Mary Nell' sound like good candidates. Others of this group are also possible, but I am uncertain which would work better in the UK, much less which are available there.

Thank you for these suggestions Tug, I will look them all up and also Arizona as my mental map of the States is rather hazy!

Hi Tugbrethil, Thank you for these suggestions! I will look them all up and see whether I think they will suit, and then go to a garden centre and view them if they are in stock. I have looked up the cotoneaster exburiensis suggested by Karen and that does look like a possibility if it doesn't mind the lack of sun.
In case of any confusion, I wrote this reply and then appeared to lose it, so wrote another and sent it, only to find this one unfinished when I logged in again!

Re cutting within 10-20 years - yes it would if you want a variety that will grow quickly to the height you mentioned.. You said you wanted a fast grower...
I like Karen's suggestion very much. Would the top still be in shade when its grown to the height you want?

There is also Ceanothus, the ones I have are rapid growers, much to my annoyance but the blue flowers are lovely....

Yes Stera, you are quite right about the topping, and I really wouldn't want the worry of that so I am now leaning toward a cotoneaster as Karen suggests or a ceanothus as Lincslass recommends but I understand the latter are short lived. It would need to grow to 8 feet before the top was in sun; I also like the sound of Wilson's holly but need to find out the rate of growth. I shall take myself off to Hilliers garden centre in the hope of viewing all the candidates! Thank you everyone for your help and ideas.
Penny

Thinking again about this I had a little Google search and found this useful link - hope it might help.

http://www.telegraph.co.uk/gardening/howtogrow/9131409/Dont-downsize-your-trees-upsize-a-shrub.html