Try giving him tasks to do as you shop -- he's more than old enough to help you shop. That distracts him from feeling he must be right on top of you and even better, it expands his self-confidence and independence.
"Sam, your Fluffies cereal is on this aisle -- halfway up, ahead there on the right. Please go get that for me and put it in the cart."
"I need to be sure I don't buy too few bagels! Could you please take this bag and count out 10 bagels from the bin into the bag?"
"Which flavor yogurt do you want? Can you get five of them and put them in the cart?" And so on and so on.
Praise him a lot when he does anything, and the further and further he has to go from you to do it, the better (within reason -- I would send my independent 10-year-old several aisles away in the grocery store that she's familiar with but not necessarily a clingy 7-year-old who might not know the store well).
If it's not grocery shopping, find other ways he can help -- fetching things from down the aisle, comparing prices with you, walking ahead to look for this or that (within your sight and earshot). Instead of just asking him for physical space, give him fun reasons to move away from you -- he'll build confidence and shopping skills without even knowing it.