Today I went and rang the buzzer of the flat above mine, and luckily the tenant let me in. I explained the problem, and she told me there was no leak in her flat. I asked if I could check, and sure enough the drain cock of the hot water tank was dripping.
She told me who her letting agent was, and I emailed them. I now have the lessee's details and a promise to fix the problem asap.
Hopefully the plasterboard will now at last dry out. Thanks to all who replied.