Harriet - it sounds like you may be trying to maintain too vertical a back angle during your low bar squats. High bar squats utilize a more vertical back angle than low bar, so as to keep the center of gravity over the middle of your feet. You've got to keep it there during low bar as well, which means a more horizontal back angle.
Surfnicky1 - The "upper body" strength required of a squat is going to be primarily in your core. You need to maintain the aforementioned "more horizontal" (but not horizontal, if that makes sense) back angle throughout the lift, without deviating, which would likely improperly load your back. Maintaining the same back angle/position of your spine requires your core, which should be activated.
I would suggest studying some form videos for the low bar squat - I am partial to Mark Rippetoe.
