Unable to authenticate with Office365 SMTP server

Problems with SMTP on Office 365

I have just had my email provider changed from Demon Internet (bought out a few times since I started, ultimately owned by Vodafone) to names.co.uk; email is implemented by them via Office365 (Exchange Online). I have been able to get Pegasus 4.72 working (I'm not using Mercury) to receive mail via both POP3 and IMAP, but am unable to get SMTP working for sending. This is not a major issue as I can use another SMTP server, but I'd like to get it working.

There are various Web sites that give the SMTP and security parameters, simple enough:
- Server name: smtp.office365.com
- Port 587 (25 should also work, but is not recommended; it gives me exactly the same authentication error message as 587)
- Login details: same as POP3, email address and password.
- No alternate address or domain name in HELO/EHLO (and using 0.0.0.0 makes no difference)
- Use SSL/TLS Via STARTTLS (neither never nor direct SSL work at all)
- Disable certificate validation ticked (unticking this makes no difference to the SMTP log)
- Don't (untick) use SSLv3 (ticking this does not help)
- SMTP authentication using specified login name and password (same as POP3). Trying prior POP3 login, and login using a POP3 name/password, do not help.
- Untick "do not use CRAM-MD5" (ticking this does not help)

Choosing some options causes an earlier failure, but with everything as above the send fails with the following SMTP log information (modified only to remove possible security risks, n is numeric,  l alphanumeric)
20:11:27.304: << STARTTLS
20:11:27.328: >> 220 2.0.0 SMTP server ready
20:11:28.496:

SSL/TLS session established
20:11:28.496:

ECDHE-RSA-AES256-SHA384, TLSv1.2, Kx=ECDH, Au=RSA, Enc=AES(256), Mac=SHA384
20:11:28.496:

Peer's certificate name is '/C=US/ST=WA/L=Redmond/O=Microsoft Corporation/OU=Microsoft Corporation/CN=outlook.com'.
20:11:28.496: << EHLO

[192.168.200.1]
20:11:28.523: >> 250-DB6PRnnnnCAnnnn.outlook.office365.com Hello [nnn.nnn.nnn.nnn]
20:11:28.523: >> 250-SIZE 157286400
20:11:28.523: >> 250-PIPELINING
20:11:28.524: >> 250-DSN
20:11:28.524: >> 250-ENHANCEDSTATUSCODES
20:11:28.524: >> 250-AUTH LOGIN
20:11:28.524: >> 250-8BITMIME
20:11:28.524: >> 250-BINARYMIME
20:11:28.524: >> 250 CHUNKING
20:11:28.524: << AUTH LOGIN
20:11:28.549: >> 334 llllllllllll
20:11:28.550: << lllllllllllllllllllllllllllllllllllllll=
20:11:28.577: >> 334 llllllllllll
20:11:28.578: << lllllllllDBL
20:11:35.114: >> 535 5.7.3 Authentication unsuccessful

If I try to log in with an incorrect password I get the same dialogue (with differences in the last numbers).
I have checked and rechecked name and password, both typed and pasted in.

I have rung names.co support; they confirm that the same name and password are used for POP and SMTP, and find nothing wrong.

 Does anybody have any suggestions, please?