I too am faced with this dilema. My wife broke the top on her favorite Denby teapot. The last time we were in the UK, we stopped in the factory to get a new top. Unfortunately, the pot was out of production and none of the replacements came close.
I was able to glue the pieces together with super glue so I could make a SolidWorks model and it would be an interesting exercise for the Tormach CNC. The thought was to make it from Ultem, a high temperature plastic often used for kitchen utensils. However, the 4" diameter x 2.5" long piece of Ultem would cost over $20/inch. Somehow, paying over $50 plus shipping seems a stronger deterrent than the idea of discarding an otherwise good teapot.
I am still waiting to find a super deal on the raw material. It's only been eight years.