It depends where you'll be staying. If you are staying in a location that gives you train access to Stampede Park, I feel you can ditch your car.
If you have not already figured out a convenient location in which to stay, you can find relevant information on the Inside Calgary : Hotel Districts page:
I don't know what you'll be doing after you've taken in the Stampede. It sounds as if you already will have been travelling prior to reaching Calgary, so I'm guessing you'll simply fly home after the Stampede.
If you'll be flying to the UK, you should be okay. Most UK-bound flights depart from Calgary in the late afternoon / early evening. However, for the sake of anyone else who reads this thread, I'll say that it's not ideal to attend the chuckwagon races on the night before your departure, if you have to leave Calgary early in the morning. The chuckwagon races are followed by the Grandstand Show and fireworks, all of which makes for a late night. It's not nice to have to get up at the crack of dawn if you've gotten to bed late. So, for people who are attending the Stampede over 2 days and who will be departing from Calgary in the morning, it's better to see the chuckwagon races on the first evening and to attend the rodeo events on the following afternoon.
Hope that helps.