Bizarre plumbing mystery - any ideas?

[Catabogus]

I have a bizarre plumbing mystery for you. We recently moved to an old and decrepit house with a view to doing it up shortly. One of the many issues is that water keeps dripping through the ceiling upstairs. I climbed into the loft to see where it was coming from, and it turns out the overflow pipe from the cold water storage tank has sprung a leak (and has been badly repaired, many times, with sellotape!).

I’ve attempted to repair the leak myself (don't want to get a plumber as the whole thing will soon be being ripped out) and put a bucket under it to catch the drip. But I simply cannot work out why the overflow pipe has water in it at all. The cold water storage tank doesn’t seem to be full when I look in it, so why is it overflowing? And, WEIRDEST OF ALL, the drip only seems to happen when it rains heavily! I thought at first that rain must be coming in through the roof and filling up the storage tank, causing it to overflow, but the top of the tank is covered with plastic which is dry.

I am now completely baffled. Any bright ideas how this is even possible?

[MrsOverTheRoad]

There's a leak in the roof. The drip is finding it;s way and running down there.

Check your loft.

[HidingBehindTheWallpaper]

Could it be condensation on the pipe?

[Catabogus]

You mean, it’s not coming out of the pipe at all?

[Catabogus]

Too much water, coming too fast, for condensation.

[wowfudge]

Is there a header tank/expansion vessel for the hot water and rainwater is getting into that and overflowing it?

[Catabogus]

Ooh...that’s a thought. The loft isn’t boarded so I haven’t investigated it fully yet. I could look behind the storage tank in case there's another tank I guess. I haven’t seen one so far, but at least that would be an explanation which would make sense! I will report back.