I have my mail set up to stay on the server for a few days, and I access it using web mail frequently when not at home. I would like my sent mails (sent from home not from Web Mail) to be accessible from web mail, as I often need to refer to  them, is it possible to set this up?

If you are using POP3 to retrieve your email then it is not possible as the sent emails only exist on your PC.

Many thanks

Gmail can be configured to collect a copy of your mail. This might/might not be of use but worth a try.

send a copy of the ones you might like to see to a trips@username mailbox, then look at them via IMAP or Web mail and dont look at them with you normal mail reader, easily configured

If you were to switch your home PC to use IMAP that and Webmail would stay perfectly in sync. Deletion of emails on either would be automatically updated on the other and emails sent from either will appear in the sent folder of both.