If you apply from the UK though be prepared for an extremely lengthy and often irritating process to become a resident through the skilled worker program. The applications are processed through the London office and the backlog is huge. The process is also staggered and your aviation medical does not count as an immigration medical so be prepared for extra costs.
Obtaining the work visa is straightforward enough (if you can get a job beforehand) but the London office is innundated with applications for residency at present and it takes AGES to get through the system.
You can still apply whilst under a work permit...I am still in Toronto on a work visa...although I applied for residency over 2 and a half years ago. I have a job with NAV Canada..I have full security clearance..I had to do my aviation medical before coming over..plus I am married to a Canadian citizen. You would think that this would be a simple tick box case so I could get my residency!!...Nope...still being processed.
PM me Oxeagle if you need any info on the application process. There are also quite afew Brit controllers living here now who went through lengthy immigration procedures hanging around on the controller forum so if you need info about it just ask there.
Good luck