They are sourced from your address books.

I can find address books but they don't show the additional email addresses under individual contacts.

have you looked in the collected address book... that is where I would guess they are.

I had already looked there and could not find them.

On the right of the address books is a list of address books. All addresses shown in the autocomplete when addressing come from one of them. There is no hidden extra store of obsolete entries.

In Thunderbird itself all those email autocomplete entries come from address books in Thunderbird. However if you are emailing from Gmail or Yahoo, or if Thunderbird is linked to a corporate email system like an Exchange server, those can add drop down suggestions from all previous saved email or from the entire corporate address book. Here are some settings to check: Check in Account settings Composition and Addressing to make sure you are not connecting to an external LDAP server. Check in Options - Composition - Addressing that addressing is looking in local address books. I would always advise setting Thunderbird not to save addresses from Sent emails to the "Collected" address book - or clean it up frequently by deleting addresses you do not expect to use regularly, and saving those you do want to the personal address book in Thunderbird. Also check the actual address book entry for specific recipients to make sure you do not have more than one email address in additional emails, and check the recipients don't exist in multiple Lists in your address book.

This has been very helpful Agnes, so thankyou. I am emailing rfom G-Mail and changed the settings as you suggested and I think this has solved the problem. One further question - I have many hundreds of entries in collected addresses. What happens to my contacts if if I delete all these collected addresses?

Glad that was useful. Check that you have all the contacts you need in Personal address book. Move them from Collected to Personal if there are any missing. Then when you delete all of Collected, you still have the important ones in Personal. What you do in Thunderbird addresses will not change how Gmail works so if you lose one you can find it again in Gmail online.