I reckon the high prevalance of the Smith surname isn't really down to a highly smith-based economy, but because it was a quite respectable profession for both social classes - high paid, possibly self employed, talented/educated - but also useful strong and dependable. So if you have to choose between different surnames you might therefore go:

• "ah my parent was a smith so i can be a smith too"
• "my parent chose to use their smith parent's surname so i will choose it too because it gets respect"

Or, maybe smiths always needed a lot of helpers and instead of taking the surname "Prentice/Prentiss" they would just go with Smith, as it's neater.

Maybe those with some experience working a forge or shaping metal had more liberty to move to different towns for work; In a new town, locals who'd lived there their whole life wouldn't need an identifying surname (assuming this is pre-surname consolidation in Britain) but the Smiths would have that as a tradename, thus advertising their services.

Presumably also, every town needed at least one local tinkerer or metalworker - there are/were like 10,000s of distinct villages all over England. So if we presume that tradespeople always have surnames of their trade and non-tradespeople (like farm labourers) don't usually feel a need to, The Smiths already have a greater share of the surnamed population in the census.

Lastly, I'm guessing the smiths had a somewhat better quality of life in relation to disease and poverty. Possibly the hot forges kill off harmful bacteria and they had "middle class" income and no vulnerability to random agriculture failure, like farmers did.

One reason why I don't think it's because "the king ordered loads and loads of people to become smiths during one particular war and we were left with an overabundance of Smiths" is because The high prevelance of the "Smith" surname is also observed in Germany, Spain, Poland and elsewhere. As Schmidt, Herrero and Kowalski, respectively. The more you know!

Or maybe it was the sexiest profession back then.

Metalsmith, Blacksmith, Gunsmith, Goldsmith, Silversmith, Locksmith, Coppersmith, Tinsmith, Wordsmith, Songsmith

Smiths and millers were common enough professions that basically every village had one but rare enough to be useful as a description. John the farmer would have been way too vague, leading to names that come from physical appearance, place of origin or relatives‘ given names.

Smiths were generally wealthier so they had a better diet and what amounted to medical care, and they were rarely put in combat because they were needed to make weapons. So more of them survived.

Smith be smithing tho