Nick here from Shopify.
Finding a supplier can often be on the toughest things when starting a store or a new product, especially for one as unique as a Muslin blanket. I wasn't very familiar with a Muslin blanket before, but they look very comfortable. 🙂
I looked into this for you and did find some wholesale suppliers for Muslin blankets. One of them is based in the UK but the other two are based out of China, which I know might not completely suit your needs since you mentioned UK/EU, but I said I would share them regardless.
Hopefully one of the above suppliers does suit your needs and you can work with them going forward.
All the best, Nick
P.S. I will also move your topic to the Wholesale and Dropshipping section of the community also. It will have a better chance of potentially getting more and better answers than the manufacturing topic.