
Because of the size of the gardens here (2 hectaires or 4 acres) I cannot use any of the deterrant techniques, (solar noise generators, plastic bottles on sticks, mothballs down the holes, etc) as this just means that they move on to another area of the garden and I have more damage than before. So I am stuck with the option of eradication (kill them all!)
I have tried the following techniques:
Smoke cartridges - hah! they push up a mole hill with the spent cartridge sitting on the top
Water down the holes - nothing
Diesel down the holes (I know its not very environmentally friendly, but I was desperate) they move to another area.

A Détauper - this is a small explosive attached to a trigger that is plunged into the hole and when Mr Mole comes along he pushes up the trigger and if he's arrived from the right direction the explosive goes off under his tummy (awww, but it's quick and painless) This is very expensive and works very well, however my insurance does not cover me for explosive devices in the garden, when there are small children running around, so this has been put away for the winter.
Worm poisoning - probably the most effective without damaging the guests. I bought a box which contained a liquid (propylène glycol) and a powder (Chloralose). Here are the instructions on the packet (translation from French).
Preparing the bait: Find 250g of earthworms, pick them up just before you treat the moles, they must be fresh (the children and I dug for three hours and found 80 worms weighing a grand total of 22 grammes (ok fine, just divide the mixtures by 10))
Let them disgorge (empty) themselves for one hour in a clean container (ok, but some of them have already been here for 3 hours cause it took us that long to find all his friends!)
Dry them on kitchen towel - fine 80 worms spread on kitchen towel across the kitchen table (how hygenic)
Dowse them in propylene glycol - not explained on the packet, this kills them all - very quickly and very dramatically, luckily the kids, having lost interest, were watching TV at this point.
Cover them in the powder.
Find the tunnels: The principle tunnels start from a ditch, a hedge or a wall and go towards the centre of the lawn. Other tunnels will be secondary feeding tunnels, these have smaller mole hills. Only treat the principle tunnels ( my mole hills are all in the middle of the lawn and all large, maybe they're all principle ones)
Putting down the poison - Make holes in the tunnels between the mole hills without letting the soil fall into the tunnel (how do I know where the tunnels are - I have made several exploratory digs, but it seems that moles do not travel in straight lines between their molehills! - hey ho, I 'll just go straight under the molehill - if someone knows how to dig without the soil falling back into the hole, please let me know)
Put in 2 - 3 worms - they're all stuck together with the liquid and the powder, I mustn't touch them with my hands because moles dont like human odeur, so here I am with my little eyebrow plucking tweezers trying to separate the worms and drop them into the holes (whilst not displacing the soil)
Now clear away all the molehills, so you can see if you've succeeded (the easiest step, I've been doing this all year)
As they say in French " On n'a pas un metier facile" (not an easy job)