The Garden Museum said the find was made more than a year ago during refurbishments.
The museum is housed in the former St Mary-at-Lambeth church and is located next to Lambeth Palace, the Archbishop of Canterbury's London residence.
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Garden Museum director Christopher Woodward said five archbishops were buried in the tomb, including Richard Bancroft, who died in 1610.
Bancroft became archbishop in 1604 and played a major role in the production of the King James Bible.
By comparison, the radiocarbon ages of organic matter constituents of the whole or partitioned loess were much younger, and are considered to represent only average ages for the particular layers concerned.
No advantage was gained by dating the carbon-enriched clay-humus fraction as opposed to whole loess samples.