*Clears throat*
The chances are it'll be Tiscali. That speedtest won't help you much - I find all of them gave me an unrealistic download rate in comparison to what I could actually get. Having said that, it will point out any serious flaws with your connection - if it's massively lower than it should be, go complain to Tiscali! (Although to be honest, I find it's better to stop talking to brick walls and just ask for your MAC code so you can move elsewhere. It's just more productive...)
If you've got 3.5mb/s broadband, you should be getting way more than 35kb/s on average. I get nearly twice that through my 1.5mb/s BT connection and a dodgy wireless router.
There's loads of little things it could be, but I'd honestly move on. You really will get annoyed with them after a while.