Any question answered...

You only tend to pay it for 10 of the 12 months. From the Merton site:

Instalments
Your council tax bill is issued in April each year. It is split into ten monthly payments (instalments), payable from April to January, unless you have chosen to pay in twelve instalments, or to pay in full in April. Your payment must reach us on or before the first day of each month.
If you get a bill part way through the year, you will be required to pay your bill in fewer instalments. The number of instalments will depend on when your bill is sent to you.