You can buy traps for moles, you just lay them in their run, then when you catch one take it a few miles away and release it.
if you,re getting mole hills on your lawn, use a stiff brush or a besom to swish the soil around, as it tends to be quite good soil they throw up, if it,s just on your soil I wouldn,t bother about it, they do very little harm, and will soon move on. Derek

Unfortunately I have to disagree with Derek, The moles I have are causing disaster in my plot. There's one in the rose garden which i would wish would stick to the lawn, but he has tunnelled under some of my roses. thus causing rocking in a couple, which means I have had to carefully replace the soil around the roots. In the borders he has tunnelled under quite a number of plants, some of which have died very quickly in the dry weather we have been having. Especially under some of my prized Clems, that I mulched with manure and compost mix that the worms were enjoying. I thought for a day that I had a sudden spate of Clem wilt. but on investagtion found it was moley, I think I may have saved a couple.
In my veg plot, one mole tunnelled along the full length of my Asparagus rows during the spring when I was unaware of the problem. then we had rain and the tunnels filled with water. All the crowns died. He has uprooted no end of the brassicas.
Unfortunately i can't use any traps as one of my dogs digs them up. But I do put garlic and vinegar water down in the holes. i have even been known to use the petrol and water trick which made him leave the area.
But once one moves out for what ever reason, another moves in, but unfortunately with the strange weather we have been having, worms are not only abundant, but also have been near the surface in the very wet periods, which is wonderful for moles.

tar

I managed to drive one out of the garden and into the dich by putting a cane topped by an empty drinks can in the molehills and each fresh one untilyou,ve sent him on his way, seems to stop him going back down the runs.....it worked for me although visitors thought I was quite mad..........

thanks