Cheshire East Council I presume.
No doubt the bills are advance notification of what will be payable for the period 01-04-09 to 31-03-10 with the first instalment not being required until April, at which time the Council will "exist".
Cheshire East has been legally tasked to be a shadow council ahead of the changeover to ensure an orderly transition. It was they who set the budget for 2009-10 and from this the new Council Tax rates. Sending the bills out during March allows a better chance of the 360,000-ish population (150,000-ish households) to receive their bills in an orderly fashion (i.e. with reduced chance of late delivery - such as after the first payment is meant to be made).