chage employer: Tier 2 timing and notice of termination

[lunakick]

I have gotten an offer from another employer (Durham University) and I currently have a work permit as a Lecturer at another university (2007-2012). I will need to apply for a Tier 2 (general) and I was told that I have enough points.

Durham says they will request the COS on the 6th of April, and according to posts on here, it usually takes a week to get the reference number for me to start my application.

I'm trying to figure out when to have my start date at the new job and when to say I'm leaving the old (where I have to give 12 weeks notice). I'm worried that if the visa doesn't come through and I've quit my old job, then the whole family will have to leave the country.

In addition, we've got flights to N. America for the 18th of May to 7th of June, so I wonder if I should apply 15th of April (hopefully COS will be here) and hope that all gets settled before 18/5/11. Or try to apply in person in May (before leaving) or June (after return). Do you think a start date of 1/7/11 at Durham is cutting it too close? Any advice appreciated! Thanks!