In outlook, tools, email accounts, view or change existing email settings.
You can choose the email account in question and select change,
go into more settings (in the botom right (ish) corner),
select advanced, click on the "advanced" tab and on that tab you can put a check in the delivery tick box to leave a copy on the server and then tell it to delete the emails from the server after X numbers of days. If you reduce that to 1 day that may do the job if they are old emails.
Is the ISP these:
http://www.fish.co.uk/
as they do webmail interface on the portal page
http://www.fish.co.uk/about_surefish/get_webmail.htm
This page may help you sort out the email probs as it tells you how to manage the inbox folders etc.