No help to you now, but you should use an email client set up to download your email onto your computer and you can then include your emails in your back up regime, assuming you have one.
You should never trust any "cloud" system to be your only storage and that includes documents etc.
There is an old adage. If it aint backed up on three separate devices it aint backed up.
As regards your email problem. I have notified the moderators of the forum about your problem. Once they have read this they may be able to help. They are a BT UK based team and if they can help they will reply via this thread asking you to contact them via a link. Once you have replied to them by the link, it can at present take forty eight hours for them to re-contact you.
I'm sorry to hear about the service you had. Can you tell me if you had a business service for your emails? Or, did you get them free as part of your BT Broadband package? Alternatively, were you paying for the BT Premium Mail service?
Let me know in case it's something we may be able to help you with.
Computers glitch. People make mistakes. It's easy to lost data accidentally.
The trouble with relying on other people to look after your data is that it makes no difference to them if they lose it.