No idea what you mean by "my BT broadband has been slammed by another company"
Those mobile dongles use the mobile phone network so are effected by excatly the same things as mobile phones are, if they have a poor reception they don't work well. look down by the clock and there should be an icon for the dongle, when your connected clicking on it should let you see the signal strength and if you are getting 3G or 2G.
If your only getting a 2G connection then it will be very slow, and if the signal is weak then it probably will keep cutting out.
You did check your area is covered by a 3G network before buying it didn't you?
http://www.t-mobile.com/coverage/pcc.aspx