Having no denomination was the rule rather than the exception for most of history. The earliest English coins I can think of that have a stated denomination are the shilling, sixpence and threepence of the last couple of years of Edward VI's reign - these have XII, VI and III respectively next to the king's head. From then until Victoria's reign coins with denominations are still relatively unusual, though they get commoner, especially on the small silver.
As far as I can work out, the first time all circulating UK coins carry the denomination in words and/or figures is around 1920, when all the gold (which didn't then and hasn't since carried any denomination) is taken out of use, and there are no crowns in circulation.
Answering your question about when the last examples were means entering the minefield of the definition of "coin" and "circulation". As said, the sovereign and its half and multiples carry no mark of value, and never have (in their UK plumage), and these are still minted. The last UK base metal coin I can think of without a denomination is the Charles and Diana crown (1981). The last coin intended to circulate that has no denomination is probably the crown of the 1893-1901 issue. I don't think crowns were every very popular in use, but the number of those and their immediate predecessors with the Jubilee head that turn up in very well-used condition suggests they must have circulated. Apart from them, all the larger silver of the Jubilee head issue carried no denomination.
