The research published by the MAC (Migration Advisory Commitee) has nothing to do with the work permit system as it is currently operating. The recommendations that they have been given are not absolutely guaranteed to form the future shortage occupation list as far as I can see anyway.
Please see here for the current shortage occupation list
And here for the current work permit guidance
Who on earth is giving you advice is what I want to know!!!
Your solicitor cannot ask for a work permit. An employer has to apply to employ you. The list that was published also does not list qualifications as such.
If you do not find an employer that will sponsor you soon, a future employer would have to apply under the new Tier 2 of the Points Based System, and then they would have to be on the sponsor's register.
If you cannot switch, you may have to leave the UK and come back.
If you have an employer with a work permit application for you, this does not have anything to do with an outstanding application for leave to remain.
What is your application for & what is your immigration history in the UK, dates & categories (eg student)? What is your qualification?
I cannot see what having an NI card has to do with anything.