I don't have a Brompton. I'll probably never have a Brompton, but if I did, I would totally take it shopping and use it like a shopping cart. That's just too cool.

Now that its in mode to bring ones own shopping bags, lots of people just fill up their own bags instead of grabbing carts. As long as your being consistent about it (e.g., only putting things in your cart and not in the pockets of your coat), I don't think you'll have a problem at most stores (at least not most stores I tend to frequent).

Cheers,
Charles