Hi
From the information you have supplied I am guessing that there is another garage the other side of your wall near where you have the damp patches.
Correct?
Plastic sheet is a good idea, however unless you put some talcum on it you may not see any evidence of drips from the overhead pipes as they can disappear/evaporate before you check next time - the talc will leave an image of the drip.
Do any of the overhead pipes run directly over the damp patches? If so, are there also joints in the pipes possibly over the damp patches. If there are joints, are they compression or soldered? Do these joints look the same as others in the garage? Are there any stains on the connectors, may be green white or brown? The stains may well look dry - particularly if it is a hot water pipe.
Do you have a water meter? If so read it, use no water overnight, draw some before for drinks and the loo if you want but do not flush. Read the meter again before using water. You need to note all numbers and make sure the 'spinner' is completely still. If the spinner is completely still and none of the digits have changed and this is very important, the last digit has not moved at all - even it still shows the same number. Anything less than this, then you have a leak somewhere in your water system.
Failing that, you are looking at drains, someone else's water pipe or ground water.
You mention a river. If you let me have your post code, I'll check out your local geography to see if there is a chance that it could be ground water. That is, after all other possibilities have been eliminated.
Just because it is not on the plans does not mean there are definitely no pipes or drains under the floor. Was your house built on virgin ground? If not then then there could also be left overs down there.
My gut feel is that the most likely cause is an overhead pipe - but in a garage - not my preference - even with lagging, water pipes are very vulnerable in an unheated space. Do the leak test first and then let's see where we go. At a guess the overhead pipes are not part of the original build? Is this correct please?
Hope this helps a bit - keep smiling - I've just been through a similar investigation and concluded that I have a ground water problem on a chalk hillside!