I think Stone Age man was asking the same question, it's been around for a long time. First you will need to stop it coming through. Then you need to get rid of the membrane and pebbles because you cannot get at it under them. Don't worry about the lawn because regular cutting should keep it down. I think the roots go down about a metre. If you are using weedkillers you will need to bruise the greenery first before spraying or watering, this will help it absorb the poison, but you will have to keep repeating the process. You can't use a hoe because of where it is, so you cannot weaken it that way.

It is a real problem so if anyone else out there knowns, I'm also really interested.

I have it and find the more I pull it out by hand the less I get and now after some years I have hardly any.

I don't know about mare's tail, but if it's the same as horse tail I can get rid of it easily.
I break it off near the ground and treat it with a good shake of malt vinegar.
After a short while it goes brown and disappears.

If malt viegar works then I'd be very surprised as the roots go down at least a metre and treating with roundup for weeks on end had very little effect. I'll give it a try though. How long have you been doing this,does it return after time

Here's something I wrote that does seem to work

http://www.flickr.com/photos/31559373@N00/4757456972/

I have also done battle with mare's tail - but as it made coal many thousands of years ago and I bought an ex aged miner's bungalow I feel some affinity to it! The main tip I would give is to first apply a wash of very hot water (it's got a protective waxy coating, I even add some washing up liquid) then when dry use Roundup. If you just keep pulling or cutting it this will achieve short term gain but in long term best to get cracking with the weedkiller in my opinion. But if you don't like using weedkiller I understand (never used it for 12 years but horse tail forced me over to the dark side!)