Hello and welcome, CCFG! I would have sent you a private message (since your question isn't really part of this particular thread - at least not yet!) but you need to have two more posts on the boards before you can send and receive private messages.
My first suggestion is that you start out on the Canada board by posting a question of your own, to get some help sorting out your family in Canada so they can, hopefully, be traced back to the UK.
Actually the very first suggestion is to talk to anyone in your family -- your parents, aunts, uncles, older family friends -- who have basic information you need, for starting.
Your grandparents' full names and years of birth are the main things you need (working on one side of the family at a time, your mum's or your dad's, whichever Billy Jeffery was in this case). And this is assuming that both your grandparents are deceased, so their information can be put here.
If your grandfather was born before 1911 in Canada (or came here as a child before 1911), he will be on the 1911 Canadian census which is free to search here:
http://automatedgenealogy.com/census11/Test6.jsp?province=Prince+Edward+IslandIt is showing an 18-yr-old William Jeffery in Prince County, but that is probably a little old to be your grandfather -- that would make for some very long generations in your family. If you were born after 1993, most likely your grandparents were born after 1930 I would think. Canada's privacy laws mean that their births and marriage will be protected information so you need to find this out from family members.
If the family has been in PEI for several generations, your grandfather's parents could be on the 1911 census and that would give some firm information to work with -- their names and ages and places of birth, and their parents, hopefully. There were 48 people named Jeffery in PEI in 1911.
Gather up all the info you can about your grandfather and post it in the Canada forum and lots of people there will be pleased to help!
Oh, and one more suggestion before you start -- go to
http://www.mundia.com and register for a free account, and then do a search for the name Jeffery born in Prince Edward Island. You will find several people with Jeffery family trees in PEI. A couple that I looked at start with two different Mr Jefferys, George born 1792 in the Isle of Wight and James born 1795 in Surrey. Now, keep in mind that not everybody has correct information in their trees and you need to check out anything you see in other people's family trees, but contacting those tree owners might be a place to start to see whether your Jefferys belong to the same families. You can send private messages through that system once you are registered.