You should look into online shops, as the Scottish apparel in London is very limited. My mother in law always stocks up on things like kilt socks when she's in Edinburgh. I was going to suggest Albion Highland, as another poster has, as it's the only shop that sells tartan I know of in London. If you were in Edinburgh, you'd have dozens of shops, but you may have to go online if you're in England.
Try tartanonline.com and scotweb.co.uk
Unless your fiance has a very common tartan, the fabric can be very expensive, and you may not be able to only buy a swatch. I looked up my tartan on scotweb, and they sell samples for £3.60, but only sell by the metre (£35-60). No clue how large the sample is, but it might be enough.