Hello!
Has anyone from Toronto (or Canada, for that matter) reserved a rental car from a company's website (e.g., Budget) to be picked up and dropped off at LHR?
Not Toronto or Canada, but I and many others have. If you have questions about which vendors are there, just go to the LHR website to get a list of vendors and compare. They have most of the big names you are familiar with, and renting is very similar in process to the US or Canada. I rented through National since I use them or Hertz for business, and I did notice National at LHR is run with Europcar, not that it makes much difference.
Do expect that the standard for cars is smaller in size, manual transmission, and diesel is more prevalent.
We tend to book through car rental consolidators, such as Auto Europe, who work with many suppliers in Europe. They may help you find more cars available in your price range. See also http://www.ricksteves.com/travel-tips/transportation.
We've gotten great service for multiple rentals using a Canadian company called British Car Rental -- including one with a LHR drop off.