If Betfair allows bots, most likely they also have some documents about how they expect bots to talk to their computers. Before trying to automate a browser and simulate a user, I would look at what direct methods they offer, as usually these are far more convenient ways than to extract information intended for humans from pages that may change.

If, on the other hand, you do not want your programs to be recognized as programs, you can try to simulate a human (or a browser, potentially controlled by a human) by using a module in the Mechanize family of programs, or Web::Magic, Web::Scraper or Mojolicious. The term you might want to search for is "web scraping" or "screen scraping".