Getting rid of celandine...

You will need to improve the soil in this area, Flosspot. The celandines will just love the damp, clayey ground. To get rid of the celandines you will need to dig the ground over and remove as many of the nodues as possible - you will not get them all. Then you will need to install some sort of drainage to dry out the ground. The ground will be improved by digging in sand, grit and humus. Celandines will still grow back for a year or two but far fewer than at present and they should be much easier to weed out.
I don't know of an easier way to get rid of them.

if you are really desperate you can resort to weedkiller like roundup which gets into the tubers and kills the little blighters. hoeing off the leaves weakends it and it eventually gives up but you have to stay on top of it.

Thanks guys. just realized I have an invasion too. wasn't here 2 years ago and although damp (Argyll) its good soil. Last summer I thought the nodules I found were from ground elder. how long will it take before I'm not a beginner? my Dad would despair!
Alif

It's spreading madly in my garden too, one patch is absolutely COVERED in the stuff and it's growing into the lawn. But it doesn't seem to be causing any harm and the yellow flowers are quite nice. Guess I've just accepted it as an early season ground cover plant!

I'm with Rydeboyz in this, I find it to be an attractive ground cover and a systemic weedkiller will (I hope) limit the spread and keep it under control.

Why do you want to kill it?
It's beautiful!

I can live with celandine under the trees but it is all through the lawn, through the rockery, and also through most of the flower beds! The garden has not been properly dug over for years and it is in its element! We also have problems with flooding from fields at the back of the house which is why the clayey parts of the garden are so compacted and full of celandine. It has to go!! I won't use weed killer so I'll do what bulbaholic has said and I'll just keep soldiering on!

Burn the b*****s.

Ten years ago we had a garden, and a patch of celandines. Now we just have celandines.

First know your enemy. The little sods procreate in all kinds of ways. The bulbs multiply underground. The flowers produce bulbils, and at every junction in the stalk more bulbils grow.

DON'T try to dig them out. You will only distribute them around the garden. And whatever you do, don't put them in your compost.

Hit 'em with a blowtorch, or an EcoWeeder, powered by butane. That way you can kill them without killing everything around them. Catch them in spring - March-April time - before they get a hold.

First blast the leaves. Then a day or so later, come by and blast right into the centre of the plant, where the leaves sprout from.

According to some people, "the high temperature flame (1000 degrees Centigrade) instantly destroys the internal cell structure, causing them to wither and die." I've never seen any sign of that happening.

Does it kill them? No, of course not - the darn things are immortal. But it's certainly bad for their morale - and it's hellish fun.