Please don’t throw them out, CM, I love antique linens and though they are going up here too, I am astounded at the prices they get in the US. As Petpntr says, if they are natural materials (cotton, silk, linen. damask), not synthetics, then they are precious, and if the lace is handmade, just think of the labour that went into them. Even if they are not perfect, antique doll collectors can use them for dolls’ clothes, craft and quilt workers can turn them into something beautiful and new, as can skilled dressmakers, etc etc. I am sure TKN would love them to bits and make very good use of them!
In terms of value, there are three values for everything antique, insurance value (what it would cost to replace them — always the highest, because you have to take into account how long you’d have to search to find something similar), shop price, which is what you’d pay for them in a high-class shop (whoever sold them to the shop would of course get quite a lot less, because the shop adds on overheads) and auction price, which is what you’d pay for them at auction, relying on your own knowledge and at your own risk, so that’s probably the lowest price, but clever shoppers can find total bargains. Auction houses take quite a large cut (25-50%?) of the seller’s price, but they are doing the advertising to your target market for you.
I think CBM is right. Take them to a posh antique shop or reputable auction house for an appraisal (tell them for insurance purposes), which you would have to pay a fee for. Then you know what you’re dealing with. Then maybe ebay, or google antique linen in your area to see who might be interested, or accept an offer from a shop once you know what their value is. I would tend to go ebay myself, as they would be exposed to knowledgeable buyers all over the country! They have an antique linens section, I’m sure, as I used to browse it! As Petpntr says, browse it yourself and see if you can see anything similar and what they are going for! Good luck (I LOVE antiques!)