Please post your Troubleshooting Information. At the top right of the Thunderbird window, click the menu button , then select Help > Troubleshooting Information. Press the "Copy text to clipboard button" and paste the information into your reply.

Thanks for the quick reply! Here is the troubleshooting information:

 Application Basics

   Name: Thunderbird
   Version: 52.1.1
   User Agent: Mozilla/5.0 (Windows NT 10.0; WOW64; rv:52.0) Gecko/20100101 Thunderbird/52.1.1
   Profile Folder: Open Folder

             (Local drive)
   Application Build ID: 20170509142926
   Enabled Plugins: about:plugins
   Build Configuration: about:buildconfig
   Memory Use: about:memory
   Profiles: about:profiles

 Mail and News Accounts
   account1:
     INCOMING: account1, , (none) Local Folders, plain, passwordCleartext

   account3:
     INCOMING: account3, , (pop3) pop.wanadoo.co.uk:110, plain, passwordCleartext

   account11:
     INCOMING: account11, , (imap) imap.gmail.com:993, SSL, OAuth2
     OUTGOING: , smtp.gmail.com:465, SSL, OAuth2, true

 Crash Reports
   https://crash-stats.mozilla.com/report/index/bp-96250f0e-6c4d-4ef6-9641-0da550170601 (01/06/2017)
   https://crash-stats.mozilla.com/report/index/bp-c6fb9086-ed95-40e1-b055-32a1e0170503 (03/05/2017)

 Extensions
   Lightning, 5.4.1.1, true, {e2fda1a4-762b-4020-b5ad-a41df1933103}

 Important Modified Preferences

   Name: Value

     accessibility.typeaheadfind.flashBar: 0
     browser.cache.disk.capacity: 358400
     browser.cache.disk.filesystem_reported: 1
     browser.cache.disk.smart_size_cached_value: 358400
     browser.cache.disk.smart_size.first_run: false
     browser.cache.disk.smart_size.use_old_max: false
     dom.apps.reset-permissions: true
     extensions.lastAppVersion: 52.1.1
     font.internaluseonly.changed: false
     font.name.monospace.el: Consolas
     font.name.monospace.tr: Consolas
     font.name.monospace.x-baltic: Consolas
     font.name.monospace.x-central-euro: Consolas
     font.name.monospace.x-cyrillic: Consolas
     font.name.monospace.x-unicode: Consolas
     font.name.monospace.x-western: Consolas
     font.name.sans-serif.el: Calibri
     font.name.sans-serif.tr: Calibri
     font.name.sans-serif.x-baltic: Calibri
     font.name.sans-serif.x-central-euro: Calibri
     font.name.sans-serif.x-cyrillic: Calibri
     font.name.sans-serif.x-unicode: Calibri
     font.name.sans-serif.x-western: Calibri
     font.name.serif.el: Cambria
     font.name.serif.tr: Cambria
     font.name.serif.x-baltic: Cambria
     font.name.serif.x-central-euro: Cambria
     font.name.serif.x-cyrillic: Cambria
     font.name.serif.x-unicode: Cambria
     font.name.serif.x-western: Cambria
     font.size.fixed.el: 14
     font.size.fixed.tr: 14
     font.size.fixed.x-baltic: 14
     font.size.fixed.x-central-euro: 14
     font.size.fixed.x-cyrillic: 14
     font.size.fixed.x-unicode: 14
     font.size.fixed.x-western: 14
     font.size.variable.el: 17
     font.size.variable.tr: 17
     font.size.variable.x-baltic: 17
     font.size.variable.x-central-euro: 17
     font.size.variable.x-cyrillic: 17
     font.size.variable.x-unicode: 17
     font.size.variable.x-western: 17
     gfx.blacklist.suggested-driver-version: 10.6
     gfx.direct3d.last_used_feature_level_idx: 0
     mail.openMessageBehavior.version: 1
     mail.winsearch.firstRunDone: true
     mailnews.database.global.datastore.id: 0ddbec85-0707-42f1-957b-082b7bbc8f0
     mailnews.database.global.views.conversation.columns: {"threadCol":{"visible":true,"ordinal":"1"},"flaggedCol":{"visible":true,"ordinal":"5"},"attachmentCol":{"visible":false…
     mailnews.database.global.views.global.columns: {"threadCol":{"visible":true,"ordinal":"1"},"flaggedCol":{"visible":true,"ordinal":"5"},"attachmentCol":{"visible":false…
     media.gmp.storage.version.observed: 1
     network.cookie.prefsMigrated: true
     network.predictor.cleaned-up: true
     places.database.lastMaintenance: 1496434360
     places.history.expiration.transient_current_max_pages: 47143
     plugin.importedState: true
     print.print_printer: Canon Inkjet iP1900 series

there is a pop.wanadoo.co.uk account which I cannot delete.

What prevents you from deleting the pop.wanadoo.co.uk account?

email is being downloaded from gmail and removed from the gmail server.

Your Gmail account is IMAP, so messages cannot be deleted upon opening. If there's missing mail, see http://kb.mozillazine.org/Disappearing_mail

I click on remove account at the menu at the bottom and it removes my gmail account and the wanadoo.co.uk is still there. Please see the image. Thanks!

I'd suggest you create a new profile, and create your Gmail account in the new profile. https://support.mozilla.org/en-US/kb/using-multiple-profiles

Use Profile Manager to start Thunderbird with the new profile.

Thanks. I've done this and made a new profile with just the gmail account. Please can you advise how I see all the emails stored in local folders on the old profile? I really appreciate your help.

Close Thunderbird.

Create a backup of your new profile. https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data#w_backing-up-a-profile

Navigate to your new profile folder. Delete the folder 'Local Folders' underneath 'Mail'.

Copy 'Local Folders' from the old profile to the new profile.

Start Thunderbird.

Brilliant help. Thank you!