Can companies legally close email accounts?

You are correct. They have always had the right to change their terms or cease to offer the service. you get what you paid for, and if they stop offering it, you move on.

Friend has it ALL wrong. I am with BT . When I signed up I had a new email address BUT -BT also sets up another email account which runs along side ours. Heaven only knows why. All my emails also appear in this account. No-one accesses it as most of us do not know it is there. If you phone BT they will tell you how to do it.

This is the one they are getting rid of as no-one uses it. Not everyone in the UK has Broadband, some remote areas are still waiting for it. I had an email from BT asking if I still wanted to use this second account. I said no thanks.

UK

your best bet is to set up a new email account with a different service such as gmail or outlook>aka hotmail and yes they can legally close the email accounts because they pay for the servers it's unfair i admit but there is nothing you can really do but change your emails over you do have a full month to do so and it won't be that hard

It is their servers and they can do with them as they please. That is the danger of THE CLOUD it is at someone else's favor that you get to use it. Many cloud services are shut down all the time.