I think if I can get a new contract from my company where my designated office is Toronto, then they can give me a work permit for Canada.
I believe Canada and UK has an agreement (specially for highly skilled IT) that the job offer does not need to go through on LIMA.
Do you think this could be a solution?
They don't give you a work permit. Your employer must file for a LMIA exemption and transfer you to the Canadian office based on your technical skills and that no Canadian or PR in your Canadian office can do the job. Assume your job is skilled. To get the LMIA exemption, your employer when filing for the LMIA exemption must show:
An advanced level of expertise is also required, which would require specialized knowledge gained through
significant (meaning the longer the experience, the more likely the knowledge is indeed “specialized”) and
recent (within the last 5 years) experience with the organization and used by the individual to contribute significantly to the employer’s productivity.
Then once your employer has completed the LMIA exemption process, you can apply for a closed work permit. FYI - sometimes the exemption and permit are refused. Are you in a highly skilled IT job...thought it was payroll?