Tier 2 to EEA2. Should I notify UKBA?

Hi,

I had been working under Tier 2 (General) from August 2011. This visa was issued outside of the UK on 20/07/2011. I recently resigned from my job and switched to a new employer. To do this I applied for EEA2 (for which I qualify), and received a Certificate of Application which confirms that I have the right to work. My last day at the previous job was January 18th 2013.

My question is, should I somehow notify UKBA that I have switched categories? I've been assuming that my previous employer would notify UKBA and that this would automatically cancel the Tier 2 visa. But there's the possibility that my previous employer doesn't bother to notify UKBA (they are not very clever...), so now I'm worried that even though my immigration status is OK somehow this could cause me trouble in the future. Should I send a change of circumstances form notifying of my change of immigration status? If so when would be the deadline for me to do it?