Why the HELL would you want to exterminate them! My bloody neighbour does - with worms laced with strychnine - and the cow has the NERVE to be anti-hunting!!
Moles leave a few mole hills - big deal! They also improve drainage and soil structure. I LIKE to see them for that reason - fields where I have moles I don't have to spend HOURS on with the mole plough!
We paid approx. 80 pounds to an expert quite afew times and for this he would make several visits until they had gone. Problem was they kept coming back after afew months.
I've found it more effective to drive the car or quad over the molehills afew times (may take up to a couple of weeks) this seems to do the trick, we rarely have any come back now. They don't seem to like the flattened soil, maybe too hard to dig through. Know it can be a real pain though and potentially dangerous for the horses legs, hope you manage to send them on their way
Get your point JG, but it is a tad annoying when you have 3 acres of field (the bottom of which could do with better drainage as it floods from the stream regularly but sadly moles seem to prefer a drier bit), a little wood and a large 300ft x 100ft garden and the ONLY place the moles are is right in the middle of the carrots and peas in the veg plot and you constantly have to move and replant everything.
Like JG, I'd leave them where they are. I might even go to Tesco and see if they sell organic worms by the pound lol. I understand about your carrots but moles are harmless, keep the earth turned over, eat all sorts of earth dwelling bugs like leather jackets and fit into their little niche in life without harm.
Moles won't tunnel in very wet ground - they'd drown!!
If it's just your vege plot that's being disturbed, that would suggest that the ground around it is rather poor quality soil and worm free. I would try creating a muck/compost heap 100 yards from your veg plot - chances are the moles will move in there and do all the digging necessary to create a NEW veg garden!