A lot will depend on the budget.
Assuming that you're not thinking of replacing the wire fence then probably the easiest (relatively cheap) would be to put in some higher posts and string wire across as the plants climb.

You could make it more decorative by using timber posts with rope swags instead of wire.

You would need to raise the fence to at least 6ft to get any sort of privacy I would assume.

Thank you both - Urbanite and Kildermorie. You are spot on! Budget is the key word here as my friend does not have a lot to spare and I am not knowledgeable to erect a 6ft fence. However your idea of installing timber posts and introducing rope swags sounds like a very tempting one, indeed! Thanks :)

I would be tempted to screen using evergreen plants. Not necessarily a hedge but careful positioning on large evergreen plants where the garden is most overlooked would be cheap and would work.

So if a window faces onto a garden seating area, plant a large plant, maybe in a pot for additional height, and it will feel less gold fish bowl like.

Evergreen plants sounds like a good and easier, cost effective way. What plants would you suggest please, Kildermorie? I think Box and other such shrubs might take too long to grow and that horrible 'fir-neighbour-causing-problem' plant would make the garden quite dark!

I have positioned 2 tallish planters (70cm from Homebase) filled with tallish plants (Bamboo and some dwarf Pines) in strategic places in between a sitting area and where next doors windows are (their windows are a good 20 metres away) so the planters are on a lawn area in the middle of my garden. I also use tender plants in pots that grow tall quickly (Musa and Canna) to provide a screen.

Box is way too slow to provide a screen and way too expensive to buy large ones.

Could you add a couple of photos to your original post? Is the fence at the top of the slope and what sort of length have you got to deal with?
If it isn't too long you could have some fun creating a bespoke trellis with long bamboo canes. If you thread canes into the wire fence they wouldn't need to go too far into the ground - there's a picture (using willow whips) on http://www.yorkshirewillow.co.uk, just verticals and diagonals to make a lattice.

Hello, I put a picture up under a question. Only problem is that I can't fing the option to add it onto here!

Fence is different from what I was expecting. I was picturing a wire link fence that you see around fields! That one is quite pretty and certainly something that climbers could latch on to. I would be tempted to plant clumping Bamboo (Fargesia) to screen out the neighbours and give privacy though or even a nice hedge of your choice.

Hello Kildermorie. The fence in the photo on my display is not the one that needs doing! I have put the question up with a picture on the Questions page. And the garden I need advice for is not mine. It is a friends and it does have a chain-link fence on either side.

To add pictures - go to your profile, click on Questions then click on update question, and you'll find options to add upto 3 photos.

Is this the garden with the overgrown bank?

Yes, it is Urbanite:) Have you seen it?

I've seen the pic in your photo section and another question you posted. I think it's worth looking at as a whole rather than splitting it into what to do about the boundaries, bank etc as separate items. It will look better if it is 'designed' as one.

Urbanite - I asked about the whole garden not just some parts of it. Do you know anyone who can suggest a design for it please?

My comment about looking at it s a whole was because you had several questions/posts on GoY which could end up with you getting conflicting advice/suggestions.
There are (probably) hundreds of books on garden design and if you use ipad/smartphone there's almost certainly an app that will help you - just search on garden design, check out thousands of pictures on GoY (not just the sloping gardens). Or good old fashioned paper and coloured crayons/felt tip pens.

Don't forget to ask your friend what they'd like to see - it is their garden (and money) after all. Get their input and they're much more likely to appreciate what they have at the end.