the horsetail is Equisetum arvense. Marestail is a different plant and is a marginal water plant.

It is a survivor from the age of the dinosaurs so they are very tough. [some people will say move!] but it can be combated with a lot of time and patience.

RHS link
https://www.rhs.org.uk/advice/profile?pid=257

Horsetail is a devil of a weed to get rid of. Kurtail Evo seems to be the chemical to use but it is very expensive.
You could try a strong weedkiller with Glyphosate. Perhaps crush the plant as it has a coating and then spray. You might have to repeat this many times though.

I seem to remember somebody saying a year or two ago that there is now a treatment specifically for getting rid of them. Its called Kurtail. I have no info on how effective it is though but any port in a storm. In the spring the first shoots to emerge are different from the later ones, having little growths that look a bit like seed heads on the top of the shoots.. These are where the spores appear so be careful to get rid of all those at least to curtail the spread until you can get it sorted.

Digging it out is almost impossible as the roots go down extremely deep.

Thanks very much for your help, I now know they’re horsetail and that I should look for Kurtail. I’ve just spent a lot of time pulling them all up. Will tackle them next year as soon as I see them.

they will reappear this year too so as soon as you see new fronds treat them.

Will do S.G. The only place it hasn’t touched is the lawn which is completely free of the wretched stuff.

Jimmy - we must have crossed - your post re Kurtail wasn't there when I posted.
Hank pulling them up is no help. Its easier to cut them off at soil level - won't kill them but could slow them down a bit...