Hi Jen. I'm sorry to be the bearer of bad news, but, from what I've read on these boards, and if memory serves, it's unfortunately impossible to get rid of mares' tail. But see what others say.

Hi Rosierose, thank you for your reply. I was afraid of that. Everything that I've read on the net says about how deep roots go and how easy it spreads. Jen

Common problem; Google 'Kurtail Gold', could have the answer to horsetail. Does look a bit expensive though.

I've even heard it suggested that its presence is a reason for not buying the house...

If you Google weedkiller Equisetum there is some good advice. The most important thing for now is to prevent the spores spreading. If you look carefully you should see that the first stems to appear have little things that look like buds at the tips. These are spore bearing and should be removed as a matter of urgency before they make the problem even worse. These stems don't have the characteristic whorls of leaves and are easy to differentiate from the later ones.

PS that looks ambiguous - Equisetum is the horsetail not the brand of weedkiller...

You could always make a feature of this prehistoric survivor - and create an area of related plants such as ferns, ginkgo tree, magnolia grandiflora (yes! Check out the Eden Project guide to prehistoric plants), monkey puzzle tree, gunnera (if the ground is damp enough) .... Add some dinosaurs .....