Apologies for nit-picking, but in fact I don't think there were any difficulties or restrictions with regard to clothing at that early stage (apart from financial resources, of course). The initial threat of wholesale bombing had not been realised, the Phoney War had started, in Germany for some time there had been rationing, but here, I don't think that life had yet changed much at all from peacetime. This was probably a bit of the "Isn't life fun, girls/let's all keep cheerful despite our worries" type of journalism.
The picture does make you wonder, though, what people were planning to do with regard to clothing when they had to resort to shelters which remained at that moment a distinct, future possibilty.
I have been trying to remember my parents' clothing at the moments when they stood, with me in their arms wrapped in blankets, at the french doors at the back of our house. Dad and my elder brother, if they weren't on Home Guard duty elsewhere, would be dressed for their outdoors vigil, Mum and my sister in whatever they were going to spend the night in as they dozed in their bunk beds made out of rough timber and chicken wire netting. Dress probably depended on whether it was summer or winter. As you looked up, the sky always seemed to be pitch black but studded with stars, whilst a bright moon cast eerie shadows in the garden. When it was quiet overhead Dad would say "OK" and we would rush down the garden and descend the steps into our sanctuary where I would be deposited in a large orange box wedged between two walls. And rapidly get back to sleep. Mum and my sister would snuggle down too, under blankets. But I remember no boiler suits or anything similar which might have been rather sensible. And certainly nothing like some of the fanciful stuff in the Mail. Just ordinary clothing and probably plenty of layers of it!
Chris