The Bagginses and the Tucks existed and they lived in the same places as the English Tolkiens!
This is Mr William Baggins Esq. from London who was buried on 27 December 1618 in the same church of St James, Clerkenwell, Islington, London in which J. R. R. Tolkien's great-great-grandfather, born in Gdańsk John Benjamin Tolkien married Mary Warner on 27 April 1777! Who knows, maybe Baggins' grave was still visible there on that day?
I have found many Bagginses in English records. One of them was Beattrice Annie Baggins from 3 Wordsworth Street Kirkstall Rd, Leeds in 1911.
I have also found the Tuck family on the same Non-conformist Bunhill Fields cemetery on which the first generation of the Tolkien family in England is buried too. See the place-name Tuckborough in the Shire of J. R. R. Tolkien!