Changing Tier2 employment and start date of CoS

Hi,

I'm switching employment (WP -> Tier2) and have alredy received Biometric Card for new employer. The Certificate of Sponsorship (CoS) start date is 10 Aug.

Despite Biometric Card issuance and offer signing, new employer is still to confirm exact start date (they are waiting for all background checks to come back), and therefore they asked me not to give notice to my current employer yet. They plan to complete all checks by 20 July.

My notice period is 1 months, therefore I need to give notice by 10 July to Stop working for my current employer by 10 Aug (start date of my new CoS).

As my new CoS/Tier2 starts from 10 Aug, I'm not allowed to work for my current employer after that date, however I might have to do that to serve the notice if I give notice not now but in 1-2 weeks, once new employer confirms all checks are OK.

New employer is aware of the situation and do not see problem with that.

Question: What would be the implications for me when I apply for ILR in future, if I work for my current employer for 1-2 weeks after new CoS/Tier2 start date for new employer?

Will UK BA ignore this 1-2 weeks "overlap" or they will see it as a serious breach of immigration rules?

Please continue in the existing topic.