I use Thunderbird under Linux Mint. I have tried this and webmail services for the ntlworld email, same result, the messages vanish into thin air....
I have just tested to see if there is a general issue with ntlworld emails not arriving in Gmail.
I sent one test message from my ntlworld address using VM Webmail to my Gmail account and a second test message using the same ntlworld address but sent from Outlook 365.
Both messages arrived in my Gmail inbox almost instantly.
One possibility is that your emails are being caught by a filter or an autoforward set up in the recipient's Gmail account.
If you are experiencing emails going missing with a number of Gmail users it seems unlikely they would all have similar filters set but it still might be worth checking with them whether they have any filters or autoforwards in their Gmail account.
You said "emails from my ntlworld email ID to people who use gmail email IDs.None of these arrive." Are there any Gmail accounts that do receive your emails?
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It would be fascinating to analyse the email headers for this 'pile of emails'. The headers should hold the key to where they have been.
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