Clothing shops, per se, are regarded as 'non essential' retailers but (assuming that you're in England, rather than Wales) you can still buy clothes in supermarkets because their primary function is to sell essential goods.
George at Asda will probably have the biggest range of kids' clothing in general.
https://direct.asda.com/george/kids/coats-jackets/D25M1G1C4,default,sc.html
F&F at Tesco might be worth a look as well though but the Tu section is Sainsbury's is definitely somewhere that I'd try:
https://tuclothing.sainsburys.co.uk/c/kids/boys-coats-and-jackets?INITD=GNav-Boys-CoatsJkts
Although Morrison's don't sell anywhere near as much clothing as their rivals, their larger stores stock their Nutmeg range:
https://nutmeg.morrisons.com/en/kids-boys?category=74603