this is not a Jaques set. Sellers often misrepresent sets, caveat emptor. As for your question, w/ a few very rare exceptions, sets manufactured by Jaques all had the mark on the King(s), including sets produced post '45.
Jaques Sets - are the Kings always Marked?

Thanks Frank. Apart from no makers name I thought the Knights were a bit too crude for Jaques - as well as not looking like any of the pics in my book

Hi Frank, I recently bought one of these later Jaques sets, bought it because it was cheap. The Kings are not marked, maybe because this is a lower quality set. Do you know when these sets were made?

Hi Frank, I recently bought one of these later Jaques sets, bought it because it was cheap. The Kings are not marked, maybe because this is a lower quality set. Do you know when these sets were made?
only sets manufactured by JoL had the mark. This set was not made by Jaques, they were just the reseller.

One of those resellers was Leuchars of Piccadilly, also based in London mate.
apples and oranges. Leuchars resold white-labeled Jaques sets as early as 1849. The set pictured is 100 years later and is a French set resold by Jaques.

I'm about to put the set pictured in post 4 on eBay - would this be correctly described as a Lardy set?

Here y'go Mr Travel
How much????
Whatever the market decides - 99p start, no reserve auction:
https://www.ebay.co.uk/itm/164099276722

Hi Matt. Coming to this thread ridiculously late but there are some rare examples of very early Jaques sets in which the King wasn't stamped at all. I have one. In general, though, and as you say, the white kings were always stamped. From the mid-1880s, both kings were stamped. As a very general rule of thumb, especially with auction houses, sellers have no idea what sets are. They confused Jaques with other manufacturers, and they even sometimes think that Staunton is a manufacturer.
I've been watching the auctions recently for old chess sets, especially Jaques sets.
I have bought and read Alan Fersht's book "Jaques and British Chess Company Chess Sets", and in this the author writes that before about 1885 the White King is stamped "JAQUES LONDON", and after about 1885 both Kings are stamped with this. He also says that very early sets are marked "J. JAQUES LONDON", and that very occasionally early sets were not stamped because they were re-sold by other companies.
The trouble is, I've see many sets on ebay advertised as Jaques where neither King is stamped. Below are a couple of pictures from an antique dealer's website that claims to be a Jaques set from around 1900.
Are there Jaques sets without the White King stamped? I'm wondering about maybe after 1945 - my book doesn't say anything about after 1945