That XS is only marginally smaller than a Lockie 40, so you might as well go with the latter.I found this one which is apparently made by Locke and is a small size, what do you think? It's a wool/cashmere blend unfortunately.
Are there any other sellers in the UK which sell good quailty cashmere zips for chest size 38" for around £300?
If it does not have to be a UK maker, you can try https://lucafaloni.com/en/gb/shop/forest-green-cashmere-zip-up. Their XS could be close to what you want and they also have a model with cables if you like that. Also no customs/vat for UK delivery.