Gotta admit I have never seen a Beatles matryoshka doll! A first for me! LOL
FYI - If initial(s) embossed on the base of a bottle match a firm name (other than a glass factory) on the front, the basemark will more than likely not be a glass manufacturer's mark. This is very frequently the case, especially with soda, mineral water, beer and other bottles of the 1880-1930 period, in which the initial(s) of the "end user" (such as the bottler, brewery, drug manufacturer, or other firm for which the bottle was made) appear embossed on the base.
The only thing I can find that they made were Hutchinson Soda Bottles and Hutchinson was out of Old Forge, Pennsylvania .