Issue with loss of pressure in shower

There's an issue with our en suite shower that is currently puzzling us, and our plumber.

Our en suite shower is making a high pitched 'squealing' sound after about a minute of operation, this is accompanied by an apparent loss of pressure, as the water comes out at a slower rate.

To make it slightly more complicated, it seems to only be at certain temperatures. I have a warm shower, rather than hot, and that's when it occurs. My wife has a hot shower (ridiculously hot in fact, steam everywhere) and it doesn't affect her.

However to make things really confusing, if I have a shower on warm before my wife, and then she has hers, the issue will likely occur for her too.

And finally, we've found if we run the tap in our en suite sink at a decent rate whilst the shower is on, it fixes the problem.

We have 2 showers in our house, and altogether 4 sinks, along with a washing machine that is piped in, and none of them have any issues with water flow.

Our plumber replaced the shower [head], but that didn't help, and actually seemed to make it worse, with it occurring pretty much immediately. The shower [head] he replaced ours with has since worked fine in another house.

He did say our water pressure is extremely high, and indeed when we turn a tap on the water shoots out, so he wasn't sure if that had anything to do with it. He's stumped and he's now asking around to see if anyone he knows might have any ideas.

I was wondering if anyone else has had a similar problem, and has any ideas how to solve it?

Our house is only about 10 years old (we've been in it about 3 years), and we've only had this problem for the last 6 months or so without anything obvious changing.

I should probably mention that I'm not great with DIY, so explaining in layman's terms might be best.