I have not had a layover in London with RTD. But I recommend checking the requirements here:
https://www.iatatravelcentre.com/
Since you have transit, select
Multicity. Select
Transit for your first stop in LHR. You have to put the next destination as well.
In the About You section, fill in your
1 - Current nationality
2 - Country of residence - Canada
3 - Travelling as - Stateless/refugee
4 - Travel document - 1951
5 - Issuing country - Canada
Hope this is helpful. I would recommend transiting through a visa-free country for RTD's without PR (like Germany or Italy) to make the trip stress-free.