If you have a BA Basic ticket and no status, I think it is a case of you would still need to pay to move a seat if OLCI did not give you what you wanted. Now luckily the algorithm does not do what some airlines opt to do, namely give you a deliberately crummy seat, indeed you may end up with a bulkhead or exit row since no-one else is prepared to pay for it. If you are in a still not willing to pay up, then what you can do is wait until about 50 minutes to departure, then ask very nicely at the gate if you can have another seat. After OLCI has closed, BA's systems don't allow for payment. Agents aren't supposed to move Basic passengers but most will do so anyway.
It's quite a long trip, and I would consider paying up, particularly on YYZ to LHR. You would be saving a lot of money compared to upgrading to WTP or business class. Daytime back to Toronto, well maybe just get lost in the inflight entertainment system.
I am not on top of how this works in Canada, but there are some credit cards on AA that get you oneworld Ruby status, this allows free seat selection at one week to departure even in Basic. Welcome to Flyertalk and welcome to the BA Forum.