Rats

We've had rats coming into our garden since last year. They finally got into the garage early this year, and my husband got into hazmat gear to clean it out and throw loads into a skip. They keep coming into the garden albeit a lot less frequently. Our garden is small, probably 6m at the longest bit and 5 across, but smaller because a garage is in one corner. If that makes sense. I have my blowaway greenhouse out there and I'm really struggling with the idea of them getting in and rummaging around amongst the plants. I'm paranoid about diseases even though I know they must be accessing the allotment along with badgers and foxes and cats who think it's a toilet. 

This is mostly a rant of course, but please give me your advice for keeping them out of the garden and/or not being so worried about disease. We have purchased rolls of rodent mesh that are 40 cm deep which we plan to bury along the fence as much as possible. We have probably useless sonic scarers. We have moved pots and things around back there to make it less hospitable and blocked up the garage access (awaiting new steel door installation). Any other ideas? Please help your neurotic internet acquaintance.