This is all so useful. Thanks all! I am in the UK and a lot of the farms / suppliers won't ship over here alas.
I got a really useful reply from Blue Diamond which I thought others would find helpful
'First, Blue Diamond only processes almonds; however, the transportation equipment used to transfer the almonds from the orchards to the processing facilities is shared with other nut growers. Many of our almond growers in our grower co-op have other tree nut orchards (separate from the almond orchards).
Let me emphasize that the harvested almonds are NOT shipped together with any other nuts; however, because the equipment is shared , it is possible that a stray walnut, pistachio or hazelnut be left behind in the dumpers.
With our tightly controlled processes, it si unlikely that something like that would get through our system and into our finished/packaged products, but in the event it does, we need to inform our consumers of the possibility with that statement on our packages.
Other tree nuts would include walnuts, pistachios and hazelnuts.'
I have one daughter with only walnut allergy and one with only peanut allergy so am navigating the minefield of sourcing nuts with minimum risk of cross contamination. Our doctors here , who are leading clinical research projects at Guys and St Thomas hosp, believe it's really important to keep giving them the nuts that they can have to prevent them developing allergies to those too. But finding nuts that haven't been processed with others is really hard.