As your boiler has a pressure gauge, it probably isn't leaking from a radiator pipe. If it was, the pressure would drop and you would have to top it up.
Looking at your plan, it's quite probable that the incoming water supply enters under the front door and runs under the floor to the kitchen. In this case there will be a stopcock, either near the front door, or where the front gate used to be when the house was built. It might have been paved or concreted over by some idiot. There ought to be a small iron lid, just big enough to put your hand down. There might also be one in the pavement, probably in a straight line with the route to the kitchen. This i where you will likely find the water meter, if you have one. The lid will be modern, a bit bigger, and possibly black plastic. It can be levered up with the handle of an (old) spoon.
It is very likely that the soil pipe runs down the outside wall from the bathroom, and the sink waste pipe runs into a gulley nearby, and the underground drainage from these runs across the back of the house and into a drain that runs past the side of your house. In a semi it may join up wuth the next-door drains and it might run down the side of their house. There will be manhole covers that give clues where it is.
The gutters from the back of the house probably run via downpipes near the corners into gullies, or possibly straight into the ground. These are likely to run past the side of your house into the same, or possibly a different, drain. Some idiot may have concreted over them. At that age, especially if you live where there was a town, dock or industrial area prior to 1945, the gullies and drains in the ground are pretty sure to be cracked and leaking. If there are signs that the concrete over them is cracked or has been repaired, this will be due to the ground sinking as a result of the leak.
As you have some wooden floors, the house will have been built with air bricks along the external walls. Please add them to your plan and photograph them for us. Some idiot may have concreted over them. If your street has similar houses built at the same time, you may be able to see their pipes and manhole covers, the builder is likely to have used the same method for all his houses.
Having looked at the picture I am inclined towards a drain or downpipe being the source of the water.
You really need to look under the floorboards near the water and see what you find.
Ask around for a local small builder. A semi-retired person will have the boards up in a jiffy, and will be familiar with the travails of the local houses.