So, you must be issued an IM1 Immigrant visa. You can only use it once. So, here's how it's gonna work
Singapore -> UK -> Canada
You do not need Transit visa as you would have a valid entry visa of Canada (your final destination)
Canada -> UK -> Singapore
You NEED transit visa because UK only consider visas of Canada, New Zealand, Australia and USA to exempt transit visa. (And you will not have a PR card to show)
Source
You shouldn't ask UK immigration. You should ask British Airways. They are the ones who are going to allow/refuse entry into plane (at Singapore Airport)