I found this absolutely bizarre. Clearly it's not illegal. Of course they can decide they don't want you to do something in their shop and ask you to leave if they don't like what you are doing, but you are not breaking the law. But could it really be company policy that you aren't allowed to write prices down?
I emailed Tesco, and this was their response:
Please be assured it is not company policy to stop customers, or journalists, checking or writing down prices in our stores. We have contacted the journalist in question to apologise and we're looking into this to ensure it doesn't happen again. As I'm sure you're aware, our prices are displayed on our website so are readily available for all our customers to compare with others, if they wish to do so.While the final sentence is irrelevent (as website prices aren't necessarily reflected in stores, especially Tesco Local or Metro or whatever they call it), the Customer Service Executive who contacted me makes it clear that it is not company policy to stop people from writing down prices. This seemed likely to be the case, though it makes you wonder why the store manager didn't know company policy. And for that matter, why he thought that the company would have any objection to people writing down prices.