Hey andrew,
Welcome to the forum!
yes - you can apply from Canada. Since you are from the Uk, hence visa-exempt, you can stay in Canada ( as long as you have a tourist visa) and apply from there, but apply outland - even if you are in Canada. For UK citizen it is much faster. THe fact that you are in Canada now doesn't change anything.
So - download the application guidelines, start reading and printing out, fill out the forms, gather evidences, and come back here with questions - advices are free here, and most people are really helpful - and we have all done the process ourselves, so it's pretty familiar... I'm also going through the UK office.
You'll need to send first your application to Mississauga, and then they forward it (once the first part approved) to London. First stage is currently 3 months, and in London it can take anywhere from 2 to 7 months.
If your case is straightforward, you don't need a lawyer, and you only need the energy to put the application together. Read the first post by Leon on what to think about, and read CIC guideline. http://www.cic.gc.ca/english/information/applications/fc.asp
Anything that is not clear / just ask!
Good luck,
Sweden