The problem is that Becstein is still around, therefore, why buy a used century old Becstein that was rebuilt while we can just a brand new Becstein that if something is broken the piano is still under warranty. Therefore, £2000 is about right.
I personally will not buy a century old piano just for the sake of having a Becstein or Steinway unless the price is low. From my experience of trying old rebuilt Steinways, virtually they are not in good condition. However, I ,one time, tried a rebuilt old Becstein with Yamaha keys, they are lovely, but I still will not buy if the price is too high. By the way, I do not really like the action of Becstein (kind of stiff).
If people appraise yours at low price, you won't be happy. Therefore, just enjoy your piano, who cares what other people say about the value of your piano. Since you are happy with your Becstein, it is priceless!