You need to contact Tiscali and get a MAC code of them. Its a long code with letters and numbers in it.
Once you get it, all you need to do is go on the O2 website and there should be a switch button instead of a new customer. In there you should be able to type in your MAC code and all your details and it should automatically switch over in about a week or so.
I did this with BT to ADSL24 and it was very smooth.
Wont be as smooth as that if Tiscali have their line on LLU with line rental as well as BB. Is the phone line with Tiscali as well as the BB?
No, just the broadband.
Question.
Would we still be able to use the Tiscali email addresses?
It's the same for every BT Wholesale or SMPF ISP - get MAC, give MAC to new ISP, get switched some point (usually around a week) later.