You're covered with NHS. Just register with a doctor once you have a mailing address (not a hostel/hotel) and if you get sick between the airport and getting an apartment then you will be treated at a hospital if need be.
When you leave the
UK to go to other places (like Paris), then you will need travel insurance. You can get this from the UK for much cheaper than Canada. I paid 50 pounds for year-long coverage with a company called Atlas, and they were fine. That was a few years ago now, but I'm sure the prices are similar for any of the major travel companies. They advertise everywhere, so I wouldn't worry about this until you arrive in the UK.
The downside to all of this is that if you die, and you don't have medical insurance from Canada, then your body will stay in the UK. Sounds harsh I know, but this is something you should discuss with your family as it could cost them $10 000 + to have your body shipped back to Canada.
The upside is that the NHS covers most of the same things you would need in Canada as well, and then some. So, dental is theoretically a part of your NHS service, but if you know much about the British it's that they're aren't known to have good teeth. You should expect a wait to get anything dental done, unless you want to go private and pay for the dentist.
Birth Control is free, and I found my prescription that costs about $100/month in Canada was only 6 pounds in the UK.
I hope this helps! Good luck in the UK this year & next.
Cheers,
Victoria Westcott