Right to work if applied for ILR

Hi, I am tier 2 sponsored migrant, employed by a private school which is going under due to the pandemic. I've been in the UK 10 years so can now apply for ILR. As long as I apply before my last working day, I can remain in the UK, but do I have the right to work for another employer while my application is considered? I've heard you can get a positive verification notice from the Home Office, but not sure if this would confirm I can only work for the employer that terminated my contract or if I could work for any employer. With priority service closed down temporarily due to COVID19, I'm looking at 6 months unemployed while my case is considered if I'm not allowed to work. The coronavirus immigration team have been no help... they don't know a thing about employment law. Thanks to anyone who can give advice or any info.

Under what route are you applying for ilr?? Presumably ilr based on 10nyears long residence.

While your ilr is pending, your existing tier 2 visa conditions continue and you can only work for your tier 2 sponsor. So no, you will not be able to work for someone else while you wait for a decision.

Ilr is not taking 6 months.