Butternut is sometimes used as a substitute, (Juglans cinera). However, it too is a North American wood, and I don't remember seeing it offered for sale in the UK, but you might be able to find a source.
A second one to consider is Peruvian walnut (Juglans neotropica, J. columbiensis, and J. autralis). Again, finding a source may be challenging.
Have you tried searching for European walnut - It too is hard to find, but you might get lucky, and it's similar in appearance? Quite a few think it's more attractive than American black walnut.
I suspect it might be easier to find some 3" thick American black walnut, but it is pretty uncommon, as you've found. You could also consider buying some two inch stuff, machine it down to a bit over 1-1/2" thick and join a sequential run of two 12"+ long pieces together to get your 3" dimension.
I suspect I've not been much help, but these suggestions are the best I can think of. Slainte.