Yes, I’m based just outside London and a mum myself so I’m also familiar with our various shops and where you and I could pick up supplies easily. But, I think anyone walking into a John Lewis with a baby wrapped in a swaddling blanket (which may be a little worse for wear at this point) would very much stand out from the crowd in there. Also, large items are usually sent to the pick up point for you, which means waiting. I don’t see a JL being a potential target store. When you start breaking it down like that, it’s not so easy IMO.
I was actually thinking more along the lines of they may not have had the funds to buy baby items, and that in itself would draw attention to them potentially. I always notice someone carrying a tiny baby in arms, remembering health visitor warnings about being careful not to fall and so on. I imagine mum and baby are inside somewhere though (I hope they are). A lone male would be able to blend in a lot more easily, so he’ll most likely be out in public.
JMO