I use the BT email app on my laptop. It generally works fine apart from being very slow to delete emails after selecting them. I thought it was linked to the speed of my wifi but we've just updated to fibre and it's precisely the same. Gmail works fine so I suspect it's an issue with the BT app. This extends my time administering emails considerably so I'd like to resolve this if possible.
Ditch the BTMail client/ app and use one of the many superior free ones such as Thunderbird.
I have been experiencing the same problem for months on my PC. It starts out okay when deleting emails but starts to get slower and slower until my Chrome browser starts coming up with wait warnings. It is like there is a cumulative problem similar to a memory leak that degrades the system.
The only solution is to restart the BT email application. If you are trying to clear down a lot of unwanted emails it becomes a real pain.
I spoke to BT about this recently. They advised that it was probably my laptop and nothing they could do. Sounds like others have a similar problem though.