I changed from Norton 360 to Kaspersky Internet Security about 8 months ago (running under XP), and to be honest I was disappointed at how little speed gain I achieved.
I suggest you recommend that your mum changes to free security software, such as AVG Free antivirus (click here) and Zone Alarm firewall (click here). They're both quite light on computer resources, and trusted by many people on this forum.
There's nothing wrong with changing from Tiscali to O2, but don't get your mum's hopes up too high for any dramatic improvement in speed. There are many factors that dictate the speed of a broadband connection, and by no means all of them are under the ISP's control. For example, the distance from your mum's house to the telephone excahnge is probably the single most important factor.