If you know what you are doing and looking for then ebay can be a good source, however study the section regarding authenticity. There are lots of people on ebay who have house clearance or selling for family members. There are a number of websites, also vintage shops and also vintage craft fairs. Here is a list of places where you can find vintage scarves and if I have shopped there my opinion.
I have shopped here a lot, their vintage buyer is very knowledgable and if you have any questions will help. What I like about this shop and why this is the place for my birthday or celebrations I tell my family to use is that the scarves come beautifully gifted in tissue and box. Anyone with storage issues this really saves having to look for boxes and buy them. Fast next day delivery. One of my favs but they sell them very fast.
this is online and also there is a shop in Soho, prices can be higher than some places but they do have good selection and are also in excellent condition. The shop is in
2 Ganton Street
London W1F 7QL
Good site, good selection and prices. However they sell out fast so you have to keep your eyes peeled.
Asos marketplace is now developing and you will find a lot of high street vintage shops also selling on here. Asos have a strict criteria for selling and it should be the boutiques where you look for all things vintage. If you are an avid vintage spotter then also the individual sellers if you know what you are looking for.