There's a film on my tea
A thin, rainbow tinted film sits on the surface, and once the cup is empty a pale ring is left round the inside.
Likely cause
Temporary hardness specifically, the calcium and magnesium bicarbonate kind. It complexes with compounds from the tea as the cup cools and settles as a film. Permanently hard water carries no bicarbonate and brews clear.
Test it at your sink
Brew the same tea twice, one cup with tap water and one with bottled low-mineral water, and look at the surface of each. A film on only one of them is the water.
What to change
Filter the water, or keep a low-mineral bottled water for the teas you drink black. A squeeze of lemon breaks an existing film up.