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Hmmm ... an adapter to fit the larger American shank into the smaller English receiver would be larger on the inside than on the outside!

There are two possibilities (that I can see):

(1) An American-shank mouthpiece should fit about half-way into the B&H receiver (assuming that the B&H shank is roughly the same dimensions as a bass trombone shank). This can work if you can push the main tuning slide in at least 1/4" (6 mm) further than its "normal" setting (i.e., where you'd set it for the smaller-shank mouthpiece).

(2) Having the receiver replaced with a larger one (or having the existing one reamed to the larger size) is a long-term solution ... but then you'll need an adapter to use any B&H-shank mouthpieces you have.

Hope this helps!

It's cheaper in the long run to buy either a Wick or a PT mouthpiece in your preferred rim and cup. I have a Wick 1 and a Wick 2 for mine: the 1 is like a Helleberg cup with a Bachish rim, and the 2 is similar to a Bach 18, possibly a bit deeper. The Wick 3 is standard issue with an Eb. With a PT, all you do is add an "S" to the end of the model number.

If it's Boosey & Hawkes, it's not SO old (1934 or newer).
With all the mouthpieces and sizes available, I'm sure that you could get one that fit properly, and not need an adaptor.