Jethro,
Does the rainwater from the garage drain directly onto your property?
If it does, then you can insist that he alters the drainage system so that it does not.
If it drains onto his property and naturally 'soaks away' into the ground before crossing your boundary then you have little chance of doing anything about it unless you can prove that the water actually comes from that source (using a coloured dye) and that it is causing damage.
That is a requirement of your permissions and it must be accepted. Garages under a certain size, construction and distance from a boundary do not need building reg approval.
There will be no danger from that amount of water either from subsidence, rising damp or flooding if your extension is correctly built - now 'ponding' water in the garden is another matter!
Brian G - who has just returned from a holiday on an island where petrol is
*3 pence* a litre - for those interested in filling up there its 5,500 miles away :-)