I had a similar problem with 3mobile last year. On connection there seemed to be a burst of activity which, after a few seconds faded away, with result that the home page would load but nothing threrafter.
It turned out that there was trouble with a nearby mast causing reduced bandwidth. Calling Three helped and I got some money back for the period that the system was down.
I gave up on the Three dashboard and flashed my dongle with Huauwei version which allows you to monitor download speeds.