Lawn Drainage

Hello, not sure where else to go to get the answers (if any) i'm looking for. Basically, when my next door neighbours moved in, they did a load of landscaping in their garden and part of that was to remove the trees and shrubs that separated our gardens. These trees and shrubs were actually ours, but as we have always had pets, when we moved in, we put a fence on our side of the trees to keep our dog from getting through to next door. 

After the new neighbours had dug out the trees we started to notice that our lawn was getting very boggy and not draining well at all when it rained. On top of that, the fence that was still in place was very unsecure and unstable in the strong winds, leaving us to prop it up with planks from our side to counteract the direction and force of the wind.

We decided that enough was enough and we needed to have a proper concrete based fence with slot in panels and have managed to reclaim the lost land (about a foot or so) from next door. 

However, because the next door neighbours actually dug down into their lawn to create a raised garden effect with a concrete patio area around the back of the house, when we had our fence put in, the workmen obviously had to work from the lowest level and i think this is what is now causing an issue in our garden. 

Lastly, when the workmen were putting in the fence, all the to-ing and fro-ing and the rain whilst they were working had turned the boggy side of the garden into an absolute quagmire! We have tried forking and putting grass seed in to try and get it back but it's worse than ever.

The water is now collecting on the surface, it's just a complete mess...but we have a nice fence....

If anyone can offer any help or advice, i'd be so extremely grateful!

Thank you xx