I would suggest T-mobile mobile broadband for you. You can consider T-mobile mobile broadband plus packages which come with 1.8MB speed and 3GB download limit below £20 per month so it can really suit your budget.
To know more details on T-mobile broadband:
http://www.broadbandsuppliers.co.uk/provider/t-mobile-broadband-internet.html
Likewise, you can also consider 3 mobile broadband packages which also come in similar price range:
http://www.broadbandsuppliers.co.uk/...-internet.html