Indeed. But ages are not included in FreeBMD until 1866, and even restricting results to London and Middlesex there are still dozens of them.
The GRO index has ages, but you can't restrict it by county - only by registration district.
There are no possibles in Marylebone, which is where they were in 1861. In Kensington there a one death of a Mary Ann Turner in 1864, but she was 29 so isn't old enough to be Henry's wife, who was already 29 in 1861. There is a 32-year-old Mary Turner in Islington in 1864, but without checking every death of a female Turner (since you can't search for Ma* on the GRO site) in every RD in London I can't be sure she is the only possible one.
Maybe if there is a really wild, wet and windy day when I really don't want to go outside I might attempt it ....