Probably they mean spoken English, rather than written English. Written languages are traditionally considered secondary to spoken ones in linguistics, perhaps because they tend to be acquired several years later in childhood and several millennia† later in history. English is normally considered to have about 13–15 vowels, if we exclude the rhotics, depending on dialect: TRAP BATH PALM LOT CLOTH THOUGHT KIT DRESS STRUT FOOT FACE GOAT FLEECE GOOSE PRICE CHOICE MOUTH COMMA LETTER HAPPY, in Wells's standard lexical sets.

But, you say, that's 20 lexical sets, not 13–15? Well, no dialect distinguishes all 20. My idiolect (a slight variant of General American) realizes TRAP and BATH as [æ], PALM and LOT as [a], CLOTH and THOUGHT as [ɔ], KIT as [ɪ], DRESS as [ɛ], STRUT as [ʌ], FOOT as [ʊ], FACE as [ei], GOAT as [ʌu], FLEECE and HAPPY as [i], GOOSE as [u], PRICE as [ai], CHOICE as [ɔi], MOUTH as [æu], and COMMA as [ə]. That's 15, or 12 if you leave out PRICE, CHOICE, and MOUTH, which are diphthongs made of vowels that also occur isolated. (GOAT is debatable, usually analyzed as [oʊ] or [ou].)

Different dialects draw the boundaries in different places; for example, dialects with the "trap–bath split", such as RP, famously realize TRAP and BATH differently ([æ] and [a] in RP). Some dialects have fewer vowels; if we consider Indian English to be a single dialect, it may have more speakers than even GA, and most varieties of Indian English have fewer vowels than 12. I haven't found a good phonological analysis, but if you know any Indian English speakers and also know phonology, you know what I mean. https://en.wikipedia.org/wiki/Regional_differences_and_diale... goes into some detail.

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† The historical gap might be much larger than this. Sumerian cuneiform and Egyptian hieroglyphs date back about 5300 years, and they provide evidence that spoken language was considered to be universal among humans at the time—there is no suggestion of tribes that lacked language anywhere in the written record. Today there are still peoples without written language, and a few who only acquired written language within the last generation. So we have good evidence that it has taken at least 5300 years. But Homo sapiens has been around for sixty times that long, over 300 millennia, and stone tools date back 2 million years. It strains credibility to imagine that the authors of the Lascaux cave paintings or the Denisovans who invented sewing were so unlike us as to lack speech; the origin of spoken language is usually dated to before 40kya. Unfortunately, no tape recorders have yet been found from that epoch, so the uncertainty of the antiquity of spoken language ranges over nearly a factor of 100. Maybe spoken language is a million years older than written language, or five million. Probably not ten million, though, or we'd be studying chimpanzee folklore.

Phonetically, English has about 9 or 10 vowels, depending on accent. Consider bill vs bike, or goose vs look.