Something tall, fast growing, adaptable, attractive, evergreen. Look at 'Thuja Green Giant'. They don't take up much space and will achieve the affect you are looking for. Another option is 'Spartan Juniper'. Either does well in full or partial sun, but must have good drainage as with most trees.

Hi Colter, I really feel for you, I too live in Norfolk and we are being inundated with planning permissions, stuffing houses in everywhere. Dreadful thought especially when you have bought a house specifically for it's lack of neighbours! You need something thin or you will lose lots of ground space and will either need to be able to get behind it to cut the back or assume that these new neighbours will be happy to cut their bit! Hedges and trees can cause so much upset. Perhaps you could put up the ghastly wood panels and cover them with Clematis or vines depending on aspect, or grow Cotoneaster which is amenable to shaping and being hacked about, it also gives you flowers and berries for the birds. Nesting sites for birds and prickles to keep out unwanteds!
Personally I would wait and see what the developers are planning on putting up as a boundary, they may be obliged to erect a quality board fence after the removal of the laurel, (make sure they use the right boundary line) which would save you money and the problem of cutting the reverse of your hedge. Perhaps you could get in touch with your existing neighbour, Council or the developers and explore this aspect. Best of luck.

I feel for you, Colter. I live in Buckinghamshire and, like your area, houses are being built on every available piece of ground.

Honeysuckle's idea is a good one. Wait and see, or put up your own fencing then cover it with shrubs, climbing plants or anything else you like. You would need to check though the allowed height of fencing but if there's no problem with that then put as high a fence as you can manage. Then plant trees.

Good luck.

How high would you want it, and how much width can you afford?

I too am really sorry to hear of you predicament. I would go along with Bathgate's suggestion of a variety of Thuja of your choice. They look good when clipped but in you case, then just let the tops grow and clip the sides. My neighbour at the end of the garden has some and although it's a nuisance having to clip the top and edge of my side, it does give good privacy. If Thuja does appeal to you, please buy the biggest size plants that you can reasonably afford rather than wait too long for them to do the trick.

what length of garden are you talking about as that will affect what you plan to do. personally I would wait or check what the developers have planned to do before 'jumping in'. Also anything you plant before the development is complete on your side may get damaged by any landscaping they do.