Yes, you can access it via WebMail as you say you have been doing, or, more conveniently, via POP3 or IMAP using a mail client on your PC, like Outlook Express, Windows Mail, Thunderbird ...
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU => 2010: Orange 16 Meg LLU => 2011: Orange 19 Meg WBC