Providing drainage for a garden which floods

My house is about 40 years old and is situated in a relatively flat area of heavy clay. If there is heavy prolonged rain a substantial amount of water collects at the lowest point in the garden. The house is semi detached and all of the drains, including those from the roof are to my neighbours house and due to the design of the property are not available to me. The owner of the house behind me believes there is a drain which runs through his garden, parallel to the rear of my house.
I would like to know:
1. Other than digging is there a way of finding where the drains are? Who would have the plans? Cost etc?
2. If there is a drain, what hurdles to I have to cross to connect to it? Permission?
3. Other building a soakaway are there any other options for dealing with the water? Is it feasible to bore through the clay until a porous layer is reached?
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