Tier 2 (General) changing employers, CoS end date

[twil83]

I'm currently on a Tier 2 (General) visa which will expire on 6th August 2017. I don't want to stay in my current job and have had an offer from another company who are willing to sponsor me (they are completing the resident labour market test now).

I had a look at the CoS for my current job and I noticed that the end date is 17th July 2017. Does that mean I can only work for my current employer until the 17th July, or would I be able to work for them until the visa expiry date on the 6th August?

I have not yet told my current employer that I have another job offer, and they have not yet applied for a new CoS to extend my visa. My notice period for this job is 3 months but my visa expires in less than 3 months. Are there any legal ramifications for me not completing my full notice period? It doesn't seem like I have any other choice since the visa will expire before then.