You've mentioned 'mostly Cotoneaster and clematis' - before you go ahead and start replanting, its probably worth pointing out that, unless they removed all the roots of your plants, they will all likely grow again. Certainly, a fencer might cut out some roots if they're in the way of any posts they're replacing, but usually, they just cut or trample down any growth in order to do the job - which means the roots will be, by and large, intact. Unless you know they removed all the roots, I recommend you wait and see what happens as spring arrives, preferably going out with a fork and turning over the compacted areas where they've stood to loosen the soil again. Alternatively, if you want a change, you'll need to extract the roots of the shrubs which are currently there before replanting.

Agree with bamboo. Wait and see what happens. To place new plantings you will have to dig out the roots which will be multiple dense root balls with very hard compacted earth amongst the roots. I have been there (many years ago) and it is a really hard job to do, something to avoid doing if at all possible.

I'm astonished that they managed to trample down almost all the established shrubs along a 30-metre boundary. I accept that a small amount of damage is inevitable, but this sounds like complete disregard for another's property.

Your neighbour offering to quite rightly pay for replacements is one thing, but who is going to pay for the 20 years of nurturing...? And for the years it will take to establish the replacements or wait for the shrubs to regrow...? Your enjoyment of your garden has been spoiled by this, so of I were you, those responsible would be receiving a solicitor's letter demanding substantial compensation...!

That solicitor will be looking to clean your, your neighbor's and the fencing contractors respective clocks. For you they will either charge you via fixed fee or charge you for every move they make right down to a fee for licking the stamps and envelopes used and the time it took to do it. The most amicable way is the one being taken now by your neighbor. If you want to take it a step further get an estimate from a professional landscaper on the cost to turn your damaged property into its most origional condition as possible. If your neighbor agrees to the cost have him sign a promissory note (there are templates available)to pay the sum upon the demand of the landscaper or another method of payment acceptable to your landscaper. If your neighbor reneges on the note there will be big trouble for him. If your neighbor does not agree to your way of settling this matter take the small claims tract at your county court. The court can also help you obtain a solicitor if needed for your small claim for little cost. Before and after photos are going to be a must whatever is done. Take note I am from the USA so it will be up to you to parse the differences in the UK if there are any pertaining to this matter. Good Luck To You!

I have had this situation many times where my clients have had fencing done and have shown a total disregard of the plants and borders that I have looked after they always get a phone call from me telling them how un professional they have been sadly most trades people now days are just not bothered about ruining people's plants, last year builders chucked left over cement all over a clients heaters, they did not like getting a rollicking off me, it's good your neighbour is going to reimburse you but tell him to get the fencers back round so you can give them what for.

Spell check whoops should read heathers.

Sadly, there is, as Julien says, nothing unusual at all about fencers wrecking borders - they always do. Some cutting back they have to do to get at the fence to replace it, but really, they are completely careless about borders and plants, usually stomping all over everything so the whole border's wrecked or, at the very least, compacted and crushed.

Trouble is, even if your neighbours had warned you, it wouldn't have made any difference - it sounds like it was their fence, and they're fully entitled to replace it when it needs it, regardless of any plants you are either growing against it or up it. And while I'm on that subject, it is actually illegal to grow a climber up someone else's fence or wall - you're supposed to erect your own support on your side on its own posts. So I'm afraid legally, they stand four square on the right side of the law, and they do seem to be amenable in offering to pay some money for any replacement plants you may choose.

Certainly, whenever a client of mine says they're having fencing replaced, my heart sinks to my boots immediately, because unless I'm there all the time standing over them and cracking the whip, devastation of any planting will always ensue.

I think the cotoneaster will soon grow back. A scattering of bonemeal or balanced fertilizer will help it.
But if you fancy a change - a good hedge of Portuguese laurel (Prunus lusitanicus) would do well - especially the variegated one. You could keep it clipped to whatever height you like. If you can get 3 foot plants, I would plant just one a meter and enjoy them as shrubs until they join into a hedge.
Or for something else really tough - Eleagnus x ebbingei, it has inconspicuous but very scented flowers in autumn.

Please accept my apologies for not replying sooner, but I would like to say thanks for all the useful comments received. I am now waiting (not for long I hope) to see if anything comes up before planting new shrubs.