You can do it by using webmail Talktalk login. But you will only see e-mails that have not been downloaded by an e-mail client like Outlook Express, Outlook or Thunderbird unless these have been set up to leave messages on the server. This is for pop3. Perhaps a better way is to move from pop to imap. With imap all messages remain on the server until purged and can be downloaded (remaining on the server) to any pc e-mail client or your smartphone or tablet. You can also use webmail for imap.
If using mail2web, as suggested by cocteau48, I would recommend selecting 'advanced login'. E-mail account will be either pop.talktalk.net or mail.talktalk.net, I suspect. User ID will be e-mail address and Password the e-mail password.