Finding Records in England for people living elsewhere

Supposing that you find an ancestor in the 1916 Canada Census who was born in England.
How do you find them in records of England or Wales? For example:

 https://www.familysearch.org/ark:/61903/3:1:S3HY-6QLS-ZN4?

You want to know the maiden name of Annie, who is married to George W Potter and  is the mother of the family in this census record. We are looking for one specific person and we do not know where she was from, only "England".

We notice that she had two children born in England, Charles A, born about 1895 and George W, born about 1897.

I would start by looking for the births of both sons in the same specific place in England. (Yes, there is no certainly that two children born to the same mother, two years apart were born in the same place, but the chances of this happening are excellent.)

A good starting point is the FreeBMD site, which lists Births, Marriages and Deaths recorded in England and Wales since 1 July 1837, https://www.freebmd.org.uk/

First let's look for all children named Charles A Potter born in 1895. We will list his given name as Charles A*, so that it will find all middle names starting with an A. We will search 1894-1896.

Then we do the same thing for George W* Potter born in 1897, searching  1896-1898.

Then we compare the two lists for matching places. Dover looks like a good prospect.

We can search the matching people for a mother's maiden surname that also matches. We can do this with a free account at the UK government site: 
https://www.gro.gov.uk/gro/content/certificates/Login.asp

If you have an account at Findmypast.com this is easier than the General Registry Office site.
https://www.findmypast.com/

Now to confirm that Annie Craig was married to George W Potter, let's try to find their marriage using FreeBMD.  We will guess that they married during 1890-1895. Voila.

When we click the link to the page number we see:

"Surname First name(s) District Vol Page 
Marriages Sep 1895
Craig Annie Dover 2a 1707   
Martin Alice Ann Dover 2a 1707   
Munday William Henry Dover 2a 1707   
Potter George William Dover 2a 1707"   

The names are listed alphabetically rather than as couples. Two marriages are listed on that page of the register book, and we see the names of Annie Craig and George William Potter, whose marriage in Dover was recorded during the September quarter (July-August-September) of 1895. Their marriage may be prior to the September quarter, but that is when it was registered with the government. 

This information should help you find them and their ancestral families in additional British records.