So is the key that if the trowel goes under them then they can be removed? If it won't they should stay? The house is from the 60s and canals not too far away.
I managed to find this pic showing brick footings. As you see, the wall gets wider as it goes down, typically twice or more width as the wall above, to spread the load.
Shoddy shallow footings are often found in Victorian houses, but if yours was built in the 1960's I think it is most unlikely to have shallow brick footings, and I was mistaken in my earlier view.