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Police checks are sent in your application package. For the UK, it is ACRO. What other country do you need?
If you go this link: https://www.canada.ca/en/immigratio...n/medical-police/police-certificates/how.html
Here it will give you the links to where you need to get your PC from. If you plan on submitting soon, then yes I would as ours took 4 weeks. Also just a reminder if its not in English then it needs certified translation

I know where to get them from. The UK one is plain, straightforward and simple. I've done it before. The other one is Bangladeshi where it'll take some effort due to how annoyingly mismanaged all such things are there.

What I want to know is if it will be the case where the police mails me the certificates and then I mail them to Canada. In that case, I can apply now. If the immigration process requires the police to directly send them to Canada without handing it to me, then I can't apply before I start the immigration application.
 
I know where to get them from. The UK one is plain, straightforward and simple. I've done it before. The other one is Bangladeshi where it'll take some effort due to how annoyingly mismanaged all such things are there.

What I want to know is if it will be the case where the police mails me the certificates and then I mail them to Canada. In that case, I can apply now. If the immigration process requires the police to directly send them to Canada without handing it to me, then I can't apply before I start the immigration application.

Again, what I said above is you must include in your application package. The UK police certificate is emailed to you and you must print it off and send with your application. For Bangladesh, I sent the link because each countries instructions are different. While most send it to you, some send directly. That is for you to check
 
I got a few extra copies from Acro and sent in one of them. Took about a month for them to arrive here in Canada (I am in Newfoundland)
 
Good information!

I am a bit unsure about the police certificates. I remember reading somewhere that you need that from wherever you've lived most of your life in the last 10 years. Between 2010 and 2020, I've lived in the UK for 8 years. Does that mean that I only need a UK Police Check?
Anywhere you have lived in the past 10 years yes. So 8 years in the UK and another 2 years for another country.