A bit of Googling has answered my own question, partly, at least.

"Welsh Music History" gives the following about 'Please to see the King.'

"This variant was noted in Hook, Pembrokeshire, from two retired
schoolteachers, Dorothy and Elizabeth Phillips, who sang it. They also
gave first-hand reminiscences of the custom, which they remembered
from the 1920s. The wren-party would go to 'any manor houses in the

neighbourhood where they would have food and drink and sometimes
money', during the period between 6 and 12 January, which they called
'Twelfth-Tide'. The wren-house was 'a little wooden cottage and
dressed with ribbons really crêpe paper and the wren was inside and
when they entered the house of course they all looked in and wanted to
see the king.'6 After the wren-party entered there was another song
referring to wassailing:
We are not dry, we can drink no small
But tap you the barrel that's next to the wall
And sing ffol-de-rol, ffol-de-rol, ffol-de-rol dee dee.
In Kidwelly, Carmarthenshire, a different form of the wren ritual was
practised. A version of the Kidwelly wren-song beginning 'Gyda ni mae
perllan, A Dryw bach ynddi'n hedfan' is to be found among J. Lloyd
Williams's manuscripts under the title Cân y Berllan (Tune 6). Both
words and music appear to be somewhat corrupt and are noted here with
slight editorial revisions. The perllan was 'a small rectangular board
with a circle marked in the centre and ribs of wood running from the
centre to each of the four angles. At each corner of the board an apple was fixed, and within the circle a tree with a miniature bird thereon.' 8
The ffiol was a bowl or cup and the reference to wassailing is
unmistakable in this song."

Tradsinger