Strange that more is not readily available on Villiers and both his appointment and tenure in Portugal.
He was the nephew-in-law to the 4th Earl of Granard.
This is an interesting tidbit on Villiers's appointment in:
Memoirs of the late major-genl. [J.G.] le Marchant. Denis Le Marchant, John Gaspard Le Marchant. Published 1841
See page 149.
Some background on Villiers and the Portuguese Army.
The Parliamentary register: or an Impartial report of the debates that have occured in the two houses of Parliament, Volume 1. Publisher John Stockdale, 1810
Page bottom of page 411 on.
As far as confirming Villiers in Portugal in May 1811, this might require a tedious search in the London Times for shipping news and court news to see if there are any details of his travels.
There does not seem to be any report to the Foreign Secretary on his going to Portugal in 1811? Presuming that Villiers went out under his instructions. He may have gone out in a non-official capacity as the tone of Wellington's letter appears, to me, to be more newsy than an official response to enquiries by a government official!