They don't do anything beneficial in the garden that I'm aware of, and you certainly won't want them in your greenhouse. Where are they causing a problem?
Mice are omnivores so are not keen on any garden pests-in the garden they are a pest themselves but as I have said elsewhere anything on legs can stroll in to your garden from your neighbours and there's is likely to be more than one.
A trap will work but is there a food source that is tempting them in-remove or deter them from that and they go elsewhere.
I had them in the house a while back ( toddler dropping food everywhere and a dog that does the same with his kibbles), ended up hoovering up about 3 times a day and used the electronic traps, that soon made them move out (we are next to fields and have the same problem every autumn), they decide to move into the house when theirs is cut down, they don't last very long though! The worst thing is removing the corpses (my husband is the biggest wuss in the world when it comes to dead things), with the electric traps you just open a dog poop bag, or carrier bag - make sure it has no holes, put the entire trap inside & open the door, the corpse will fall into the bag, double bag it & bin it. I like them as they have a green light on when armed, which flashes red if they zap something. I always get one or two in the autumn, refugees from the fields.
Is it a house mouse? Or are you lucky enough to have a Field Mouse/ Wood Mouse http://www.animalphotos.me/mammal-wood1.htm , or even a little Bank Vole http://www.mammal.org.uk/index.php?option=com_content&view=article&id=318&Itemid=353 in your garden. If it's a field mouse or a bank vole there's no need to worry, it's just part of the wildlife that lives around your garden, it will do little if any harn.
If it's a house mouse or even a rat, then trap it or call in the pest control people.
My next door neighbours have chickens and we have had more mice since then. The little darlings were nesting in a compost bin and i only found them when i turned it out. It was like a scene from alien, all these tiny baby mice crawling around i felt quite sick. Luckily i have a cat that is a good hunter and pointed him in the right direction. If it happens again i will lock the cat flap so i dont get any presents.Your local council should have names of pest control people. Or you could get a cat.
I've just been sitting on our garden bench under a tree watching a little Woodmouse scurrying back and forth under the bench collecting seeds (mainly ash keys) - he/she is taking them under the fence into the next garden - probably laying up a store for the winter
Hi on an allotment they are definitely not required our allotments have a lot of plant damage due to mice we just suffer them were outnumbered
We occasionally get rats at the allotment when this happens the council get involved and put down poison. Not at all nice. think i can cope with mice better than rats. My cat Lennie decided to bring in frogs now, have you ever heard them squeal? and why does he have to do this in the middle of the night. The pleasures of having animals, i wouldnt be without them
As long as they don't come in the house I'm content to let them be.. I think I'm turning into a Buddhist ,I really don't like killing anything. Plus if you claim to garden for wildlife - as I do - you have to take the cute and beneficial with the not so cute and beneficial. Regards cats bringing in stuff, I have a cat flap that only works with their microchip. While Mum cat isn't bothered about catching anything, the son chasing anything that moves - mainly leaves and flies fortunately - but negotiating the cat flap seems to deter him from bringing stuff into the house. Plus it stops other cats wandering in.
Anyway they say you're never far from a rat so I imagine it's pretty much the same with mice.
Have tried the cat flap with the microchip was ok until i got Lennie, talk about paranoid last time i took him to vet ended up gettting bitten. Not good. Pleased to say no mice yet this week but it is only Monday. My Mum used to have a dog and kept the dog food in cupboard under the stairs, she ended up with very fat mice. Ended up calling pest control in he came disguised as the dog warden. the mice were coming in through the air brick. She is now mouse free.
We found a dead mouse floating in the water butt one day last week. Thought the cat may have flicked it in from the flat roof nearby, But the next day there was another one. Do you think they run along the gutter and fall in or are they practicing the crawl ready for the Olympics?