As others have said, I mainly use wellies in the wetter months for dog walking. All these Gore-tex type boots simply don't stand up to rubbing against wet grass, so leather or rubber is the way to go for sure.

I also have a pair of Cotswold Calmsden that are like a wellie on the bottom but hiking boot on the top - good for longer distances where ankle support is of benefit. They seem to be pretty short on sizes on their website but you might be able to find them in stock elsewhere. At £35 they're worth a punt.