Just finished almost exactly the same with mine – Reeds are impossible to play football around.
Fishbone trenches leading to a main gully which I've hooked into the drains, in each I've used proper drainage piping (it has loads of slots and stuff in it. Then I've added a lot of massive aggregate/stones layers, then covered over.
I've also in the process of building some raised beds so that we can grow some veggies and stuff. Garden is a lot drier (I placed my trenches closer than suggested, ended up costing me an extra £300 or so and it's probably overkill but I didn't want to have to be going back to it all again in 2 years time or so) so far – although we haven't had the monsoon weather since it's been completeed to be able to assess it properly but soil/clay above the main drainage ditch has cracked it's so dry.
I'm just trying to source some agriculteral gypsum to convert the clay to sand, I've 4-5 tons of well rotted horse manure – that with a decent amount of grit should mean that I have a half decent soil that allows me to play on the garden I paid for.