Mystery damp patch - please help

Hoping someone here can help...

I discovered a damp patch on our internal kitchen wall yesterday. It appears to spread up from the skirting board and then forms a circular shape about 12" in diamater. On the other side of the wall is the living room which also has a damp patch on the lower wall, although strangely it isn't exactly opposite the one on the kitchen wall.

We had British Gas out today and they couldn't seem to figure out the issue. He checked the hot water tank in the loft and no water was refilling into it so he thought it might not be from the hot water system. All he could suggest is that someone come and looks at what's going on under the floorboards. Here's the other issue. We have wooden flooring so began to pull an area of that up adjacent to the living room wall. This was not easy. We have stopped this now as we just feel so unsure as to what to do. The actual floorboards under our wooden floor run width ways across the room so we are beginning to think we may have to take all our wooden floor up to then lift the floorboards.

Any suggestions on what may be causing our damp patches on each walls? Would a builder come and provide access for us for British Gas as we are totally clueless as to how to do this properly and now just have a wet wall and a living room without a wooden floor. Any suggestions or advice would be greatly appreciated.

Thanks.