All shared hosting packages are limited to 400MB per mailbox, but sometimes this is not enough.
We offer the option to upgrade to a “premium” mailbox, which gives you 2Gb instead of the 400Mb you get with the standard mailboxes. The cost for a 2Gb premium mailbox is £10 + VAT per year. If you need more space than that, you can add increments of 2Gb for £10 each up to 10Gb (so a £10Gb premium mailbox would cost £50 + VAT per year).
Note that premium mailboxes are upgraded (and billed) individually, so you could have some mailboxes with standard storage, some premium with 2Gb, some with 6Gb, and so on.
Im afraid that this options are not available directly on the hosting control panel, but if you can just let us know the mailboxes (email addresses) that need to be upgraded and to what size we can help you with the upgrade.
On the other hand, also note that you can use a local mail client (Mozilla Thunderbird, Apple Mail or MS Outlook for example) to download messages to your computer and clear up space on the server.
To find out how to set up your mailbox on a mail client and download messages from the server check out this article.