I'll have a crack at this, because I have an idea I want to get down in writing.
The obvious question - have you chatted to your neighbour about whether they would remove their conifers, and you could offer to help? They can only say no thanks. Could you offer to pay for a new hedge if they pay for taking them out? Cheaper than a fence.
Trim 'em back as far as possible before you start - to the boundary is best if it won't kill the tree, and you'll need a way of trimming them once the fence is there if they start to push it over or to keep them in check. A removable-in-sections fence, or holes for a hand + secateurs might do that.
I reckon you are into £100 for the brush screen for 14m (though reed is cheaper) plus whatever structure you will attach it to. Screen won't last very long - a few years.
You could do a trad closeboard/vertilap type of fence. When I do one of those with concrete posts plus gravelboard plus Postfix plus decent panels it costs me about £20-25 a metre for materials plus hard work fixing it.
I have 2 cheaper suggestions using ranch-type fencing.
Do a horse-paddock type fence, made from round 4" or 5" posts and (probably) 4.8m half round rails. From an *agricultural* supplier 5"6" tanalised posts would be about £1.50-2.50 each. You would need 2.4m, which would be more like £4 each. Tanalised half-round 4-5" rails would be about £6-8 for a 4.8 section.
Collect in a 5m trailer or take a saw and chop the rails up on the spot to lengths you need.
The materials are cheap, and you could create the visual block using extra rails, or hang your brush screen on it.
If you did it with posts at 1.5m centres, and used the rails like an elongated chequerboard in 1.6m sections (to allow slight overlap at each post), you get an interesting effect, and I make that 6 rails and 3 posts (plus one at the end) per 4.8m section, or about £50-£60, which gives £150-£200 for the whole lot including screws. And it would last much longer than a brush screen, which could be eg ruined by a dog in a few minutes.
Alternatively you can just do one or two rails and attach a screen.
You just bash the posts about 2'6" or 2'8" in (using a post-rammer will help a lot - and can dig a hole + Postfix if you need extra strength), and attach the rails with a decent drill-driver and timber decking screws / normal timber screws / external quality (ie coated) coach screws - one for each post/rail joint.
That will give you about 5'4" posts, which you cut off at the same height, saving a need for precision post-bashing, at 30 degrees if you choose, and coat the end to help protect from water.
If you want a coloured fence, spray or paint it all first.
Bingo.
- Ferdinand