Big thank you for your advice kiwimummy and Goldhawk. Sorry I meant to reply a little while back and just getting round to it now. Thank you

The closest person gets the place. You apply through your local council, and ask for the Wandsworth school. Sometimes the wandsworth school also has additional forms to fill out so you might then need to send the forms to Wandsworth direct.

The person closest gets the place
The borough doesn't matter

Hoping for some advice based on experience or knowledge please.
I live on the border of Lambeth, but my closest primary school is in Wandsworth which I have visited and liked. I know admission criteria varies by school, but the highest qualifying factor at my level (after siblings) for this school is distance with no mention of borough. My question is... if a Lambeth resident was closer by distance than a Wandsworth resident, who would be offered the (available) place? If it is just on the criteria laid out by the school, I think it would be the Lambeth. But I am aware that each borough has a duty to offer a primary place at one school within their borough, which might mean the Lambeth resident is bumped to one within Lambeth. Any advice much appreciated.