Posted: 30/09/2017 at 18:30
I garden in a Scottish valley, also on heavy clay .... so I am familiar with the "squelchy" lawn issue.
One thing I've found really helpful was to create a bit of an island in one of the wettest lawns and plant a small copse of trees / shrubs that like wet conditions. The idea is that they will take some of the moisture out of the area and help dry up the surrounding lawn.
So far so good .... and the trees are not that big just yet so I'm hoping for further improvements.
Not sure if you've got the room to consider this.