Pretty much every paid for web host supports uploading your files on any connection. most web designers, if they have the choice, will always use broadband since dial up becomes a pain for regular site uploads.
Take a look at Web Mania click here
Hosting is £20 plus VAT per year and you get all the bells and whistles for the account that you might need.
I use BT as my ISP and they allow me to upload or download via FTP on any connection I like (dial up or broadband) to the free space they provide me.
A paid for host though, offers all kinds of useful additions, so I'd suggest you consider it.