Thanks.
We tried it on an upstairs bath, single spout.
We blocked the outlet, as best as possible, using a marigold glove. Not a great solution.
We opened both taps, with flow from just the warm tap.
After maybe a minute of holding a hand tight around the marigold glove wrapped around the outlet and spout, we let go.
We repeated that a few times.
After a few tries, we turned off both taps, then opened the cold tap. There was warm water flowing out of the cold tap, but eventually, that flow turned cold, but it is a slow flow.
We kept at it in the bath, opening both taps, running the warm flow, blocking the warm flow, and eventually things got better.
The toilets have now filled.