This 2016 article says the latest count for Britain and Ireland was 500,000 Smiths - only 100,000 more than 1881.
www.bbc.co.uk/news/uk-england-38003201
If you have access to Oxford English Dictionary databases via your county library card you may want to have a look at the entry for Smith in the OE Dictionary of Family Names of Britain and Ireland referred to in that article:
I think of Smith as a quintessentially British and Irish name but of course it has corresponding versions in other countries: Extract from the book:
The English surname has absorbed, by assimilation and translation, cognates and equivalents from many other languages, including Dutch Smit and German and Jewish (Ashkenazic) Schmidt.
Early bearers:
Franz Smith, born in Germany, in Census 1851 (Marylebone, Middx); Abraham Smith, 1857 in Great and Hambro Synagogue Births (London); Peter Smith, born in The Netherlands, in Census 1881 (Swansea, Glamorgan); George Smith, born in Sweden, in Census 1881 (Wavertree, Lancs); Frederick Smith, born in Dresden, Germany, in Census 1901 (Hammersmith, Middx); Samson Smith, born in Russia, in Census 1881 (Middlesbrough, NR Yorks); Harris Smith, born in Poland, in Census 1881 (Saint George in the East, Middx); Jacob Smith, born in Poland, in Census 1881 (Bromley, Kent); Hyman Smith, tailor’s machinist, born in Poland, in Census 1891 (Norwich, Norfolk); Wodak Smith, hairdresser, born in Poland, in Census 1911 (Islington, Middx).