Will I have to pick up my luggage and recheck it if I have booked a connection with to different tickets separate airlines?
I will be flying from England to the US (on one ticket) and continuing on to Canada (on a different ticket and airline).
Depending on the policy of the airlines, you may be able to get both boarding passes in England, and have your bag tagged all the way through.
You will still need to collect it in the US and take it through customs, but the process will be simplified.
I've done this quite a few times. I've often had one ticket (eg: from SYD-LAX) booked on Qantas, and another ticket (LAX-???) booked on American. Because they're both in the oneworld alliance, they will check you through even if it's not on the same ticket.
When I've done this my bag has been tagged to my final destination and I've received all the boarding passes in Sydney. When I get to LAX I simply clear immigration, collect my bag, leave the customs area and then drop my bag off again. As I already have my ongoing boarding passes it's just a matter of proceeding to the right terminal (usually T4 for me), clearing security and then relaxing in the lounge until my next flight.
The answer to both questions is: Yes.
US has no airside transit as explained in the question I linked as related, so you will have to clear the passport control, pick up your luggage and clear customs and then go to the connection counter once you exit customs to re-check the luggage to your destination in Canada.
