>A study here showed FWIW that drivers give less room to cyclists wearing helmets.

Just like any other measure... whatever action is taken, is taken against a current situation. Next time, it may work differently, because it has changed the situation the first time. There is no neutral observer.

>I have started cycling to my local supermarket. I may have to get some panniers though as you can't get much in a rucksack.

When we came here, I got an old car, so to have transportation until we manage. It lasted a few months, and then when it broke we were pedestrians for a few weeks. One rucksack (ordinary, not mountain climber's or hunter's) can take two gallons of milk, and about as much of other stuff on top of it.