Is it true that "tuppence" refers to a woman's vagina in British English slang? If so, why?

I don't know if you can call this answer "masterful," but here goes.

This article (entitled: "Snatch," "Hole," or "Honey-pot"? Semantic Categories and the Problem of Nonspecificity in Female Genital Slang.) is quite an extensive study on many, many statistical phenomena and anomalies when it comes to, as they call it, female genital slang. They also compare these slang Female Genitalia Terms (FGTs) by category to Male Genitalia Terms (MGTs).

This article is very extensive, so to highlight what they have to say about the term "tuppence" (which here falls under the "money" category):

FGTs contained both explicit (e.g., tuppence, thruppeny bit, Mrs Penny), and implicit (fur purse, pocket book) references to money. In most terms, the amount of money was very small, suggesting reference to money rather than to value. Many FGTs not coded with this category (e.g., fish, lettuce, quiff) have, historically, meant money (Wentworth &. Flexner, 1975), and many have simultaneously meant prostitute--Green's (1999) money category is identified as the money-maker. These terms suggest women's worth and value to be in their genitalia, and commodify the genitalia as objects to be purchased. Indeed, commodity was a sixteenth century British term, now obsolete, for the genital area (McConville & Shearlaw, 1984).

Thus, as @Garet Claborn intimated, this term seems to derive from referring to prostitutes, specifically cheap ones, and as they say points to women's worth (at least the opinion of the times) being in their genitalia.

With reference to your mention of whether or not this word enjoys usage, as you say a quick Google search will yield a number of hits connecting the word "tuppence" to a female genitalia reference. As for how widespread it is, a discussion on this forum suggests that it's not a very widespread and widely known word, one user saying the following:

I'm guessing that as Mummy, Walt Disney, Agatha Christie and my other half (parents from West London, raised in various locations across Europe) and the Online Oxford English Dictionary do not know the "front bottom" meaning [referring to tuppence], its geographical spread is limited.

Hope this answers your question.

Anecdotally I can say that it's correct, since it's how my mother used to refer to mine when I was very small ;) I think in general it's used with small children because it's a "polite"/neutral word, and if the child uses it in company, or at school or whatever, they're not going to get into trouble because of it.

Two pence used to be enough to buy yourself a nice meal once upon a time, and apparently more than that. From the bit of research I could dig up, this seems to be a slang which was born out of cheap prostitutes.

For some reason basic search results seem to suggest this has over time turned into a term used for children. Perhaps the effect of euphemising through 'old timey' phrases.

There's not a great wealth of information out there on it, but it is plain to see that British folks have heard the phrase coined that way.

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...interesting.

And thanks Martin, for that clarification which spawned my research lol. Aren't you so proud?

I think tuppence falls into that special subclass of euphemism where it's all but meaningless to look for the etymology.

Parents often promote these words because they don't want to teach their children known vulgar terms as used by adults. They only expect the chosen term to be used within the family (and maybe with the family doctor).

Many parents get embarrassed if their children bandy such words about in company, but this 'prissiness' is somewhat alleviated if the word is manifestly childish (so winkie is better than John Thomas), or sounds like part of the family's private vocabulary (Aunt Judy is better than Front bottom).

I'm sure any family doctor will have come across a vast number of words dealing with private parts, bodily functions, etc. Many of which will be peculiar to one or a small number of families.

There aren't many 'definitely childish' words for vagina with general currency. Possibly because there's nothing much to see - and therefore less need to refer to it than to a penis. In the absence of a handy childish term, parents often just coin their own words, or use one they think most other adults won't be familiar with.

If more teenagers and adults start using tuppence amongst themselves, I'd expect less parents to use it with their children. They actually want oddball meaningless terms with no known etymology.

I'm not inclined to believe tuppence derives from the price of a cheap whore's charms in the first place, but if that were true and became common knowledge I'm sure most parents would avoid it like the plague.