If your driveway is in the shade most of the time no matter what you do will be a temporary fix.

I know how to kill the moss, but how do I remove the dead remains without removing the gravel, is what I want to know.

Brushing removes the gravel as well!

Our tarmac has about an inch or so of loose gravel on top of it.

Even worse is the fact the we do not actually own the drive, even though it splits the garden in two and goes nowhere.

When you said “ our drive “ I assumed that it was a part of your property. Why are you putting your effort, time and money into a property owned by someone else unless it is part of a contractual stipulation? Personally, I would notify the owner that the drive is unsightly and request that this be remedied by whoever possesses this property. If action is taken, fine, if not, well, municipal complaints are frequently known as stones that can gather a lot of moss...

We sort of half own the drive. Under the exclusive use claim to the Land Registry rule, the drive will be ours in 6 or so years time. The people who had this place built, bought the land on either side of the drive, but not the drive itself. Don't know why. We have no idea who owns it at present and since it cuts our garden in two and we see it all the time we would prefer it to be clean. The worst moss/gravel problem though is on the part of the drive which we do own.

I do not live in the UK. Where I do live in the USA there are hydro power brushes that can be rented that are specifically made to clean moss off of gravel drives. I do not know how old you are but this machinery needs some muscle to get it from point A to point B. I would suggest to find a landscaper that would provide this service if the price is right for you. Otherwise, you will have to accomplish this task manually which is I might say from personal experience a real (forgive me for using this word) bitch.

Same problem as always. A brush of any sort removes the gravel. All I want to do is to be able to put back the gravel afterwards with out the remains of the moss in it. I could buy clean gravel, except that it would have to be delivered to the bottom of the drive and barrowed up to our area and I cannot find a supplier locally of small limestone gravel as used on tarmac drives.
Thanks for trying. I think I will just kill the moss with Moss killer and put up with the mess that leaves.

Would burning it off help? If it was all thoroughly charred it might fall to bits and get blown away in the wind? Hope springs Eternal...Of course the worry that you might melt the tarmac is neither here nor there. But then if you did melt the tarmac the gravel might stick to it and then you could brush it. And pigs might fly. It was a nice idea while it lasted and it might have raised a smile at least...