But for your query. A modified yes, as far as I'm aware, definitely more defined words or dictionary entries than say French or Spanish. Our dual language inheritance - French and Old English, and the English habit of borrowing words from all other places or realms (such as science - or making up words from classical Latin or Greek) has produced a huge lexicon with multiple synonyms and shades of meaning.
in the case of Japanese and Mandarin, how would you define a word? And what about German that can make a word from smaller units almost at will. So, the claim the world's largest lexicon is probably challengeable because of these difficulties, as you have, but it all depends on how you define a word, a lexicon or a lexeme etc. As for "vocabulary", that word now seems to have been abandoned by lexicologists, yet still commonly used by the general public. Our discussion is but, at least in my case, an almost totally uninformed one, but when you get the most renowned lexicologists on the planet to discuss or argue the matter, they won't agree either.
I have both books by David Crystal at home, "Cambridge Encyclopaedia ofLanguage" and "The Cambridge Encyclopaedia of The English Language", fascinating books and if you're in any way interested, and as an English speaker you might be, you should have both to dip into. I don't think he makes a claim that English has the largest lexicon in the world, except to say it is very large, and examines the difficulties of working out what that lexicon actually is, even in English. He writes it is difficult to think that the modern English lexicon can count any less than a million separate "lexemes". Both books a fascinating and easy to read, well illustrated too, and as I said, great to dip into. .
https://www.davidcrystal.com/GBR/Book-Detail/?bookId=44
Mine is the second edition and already a bit outdated in the way our language keeps evolving. I do worry a bit about this, some people see it as a strength, I'm not so sure, it can be disconcerting, causing language difficulties even between living generations, never mind making it so much harder for classical literature and writing to endure or be intelligible. There's something to be said for a language that present day inhabitants can read their old writings from hundreds of years ago, as in Icelandic for instance. Still English obviously has some advantages, otherwise it would not have become the modern lingua franca.
https://www.cambridge.org/us/universitypress/subjects/languages-linguistics/english-language-and-linguistics-general-interest/cambridge-encyclopedia-language-3rd-edition
So to rephrase my comment, even in a language with more than a million defined lexemes, I am unable to construct a meaningful opinion on our British and Western leadership. Will that make you happier? Cheers. JKM