Bahrain was using British postage stamps with overprints in 1952 when Queen Elizabeth II came to power following the death of her predecessor, King George VI. Bahrain was, at this time, a territory of Britain.
The stamps of Great Britain, including those with a portrait of Elizabeth II, were used (with overprints) until 1960, when Bahrain began issuing its own stamps.
Check the current selection of Bahrain stamps featuring Queen Elizabeth II here, which represent the latter part of England’s colonial days. Selection is refreshed often.