If the British are going to move into the region in the 1840s (they colonised the Falklands in 1840) then wouldn't they rather take all of Patagonia rather than settling for just Tierra del Fuego, Patagonia was only fully colonised by 1883 with the conquest only beginning in the 1870s with general Roca's the conquest of the desert and Chile's occupation of Araucania. Could the British spin the Welsh colonial scheme in Patagonia so that the colonised lands are claimed for the British Empire rather than the Argentine government? I know it was an effort to escape Britain and preserve the Welsh culture overseas but what about a joint colonial venture whereby Britain promote's colonists from Wales and the Scottish Highlands to settle the region (using displaced peoples from the latter stage of the Highland clearances) or would it be easier to just have it be another penal colony? I have seen people say that the British could not support another settle colony and this is why Patagonia did not become a settler colony, that the people where not there for migration but between 1851 - 1901 the populations of England, Wales and Scotland almost doubled going from 20.6 million to 34.9 million. Today Patagonia is a region with just under 2 million people so it should be possible for Britain and Ireland to provide enough people to create another Westminster style dominion and this is not even taking into consideration migrants from other European and South American nations.
The governments of the time did not see the value in the proposal or were simply too busy with colonial ventures in Australasia, Africa and Canada along with imperialist wars in Asia, there was gold in Tierra del Fuego and Patagonia could provide another region to export agricultural goods in a similar fashion to New Zealand so once gold reserves are depleted then investment is made into sheep and dairy farming and the exportation of wool, meat and dairy.