There is a list of the main off shore islands here http://www.know-britain.com/general/islands_of_bri tain.html
there are probably many more depending on your definition of island, places like Rockall which are barely big enough to sit on plus countless others
And of course the island comprising "mainland" England, Wales and Scotland is also part of the British Isles. You may wish to look at another page on the above website - http://www.know-britain.com/general/great_britain. html
- which very helpfully explains the difference between the expressions "Great Britain", "British Isles" etc.
I don't know the answer, but I remember a quiz question many years ago being, "Which country of the world comprises more than 1000 islands?" The answer (which amazed me) was Scotland. Hope this helps