@New_To_UKwrote:Remove the account on all your devices first - then set them up one by one with the new password - this should work.
I don't agree with removing the account on any device - there is no specific need for this.
I had This very similar problem; I wanted to link my email to BT ID & it failed - I thought changing my password would fix it & then found (after password change) that only webmail would work - I could not access my mail in any APP,
I contacted BT & they said it was an issue on their server - this morning all is back to working fine for all my devices (iPad/ iPhone/ Win10 mail / Mac etc etc).
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What I did observe is that adding IMAP account to say iPad with my new password failed (until BT fix something) - However, during my frustration I tried adding using Yahoo with BT credential (as noticed on webmail it had my email address as x.btopenworld.com - AND bingo - it worked
so maybe if anyone here having problem try this.....