Can't do anything about bone dry but see our project on French drains and soakaways for when you are flooded. French drains can be anywhere in the garden they do not have to be against the house and a pipe to a soakaway can be laid in them or at the end of them.
I have the same kind of garden/ground as you. I think this is typical of heavy clay areas. When I moved here (five years ago) the lawn was bald! Someone advised that putting a layer of sharp sand on the soil before I laid the turf would help to break down the clay. Now, twice a year at least I spread several bags of sharp sand across the lawn (as well as a mixture of compost, top soil and grass seeds. I don't mean to literally cover the lawn, just scatter. Last year the lawn came right and has been green from corner to corner since. Drainage no longer seems to be a problem either however, I do still get the odd dry patch but this is overcome by regular waterings. The guy across the road from me is an avid gardener and the rule to follow is: When you have finished watering the garden, water it again!
I hope this helps you or anyone else as much as it helped me