Since posting I have followed advice froma another source and downloaded and run something called Malwarebytes, which found something in the registry called "Disable Security Centre", two copies. These were removed and the computer restarted.

Still, I could reach the google page from my favourites menu, but when I entered the search and either pressed enter, or the search button, up popped the download option again.

There is one difference between the two computers. When I started usuing BT internet, I loaded their software on the Tosh, though I don't use their homepage or go to their site much. On the Asus, I just entered the connection manually.

I've updated McAfee Security centre, and am about to restart again.

Penny