It's actually a Welsh choir that sings the bit in Welsh. What they are singing is called Sosban Fach.

Here's a Welsh text and an English translation.
Welsh                                        English (literal translation)
Mae bys Meri-Ann wedi brifo,                Mary-Ann has hurt her finger,
A Dafydd y gwas ddim yn iach.                And David the servant is not well.
Mae'r baban yn y crud yn crio,                The baby in the cradle is crying,
A'r gath wedi sgrapo Joni bach.                And the cat has scrammed little Johnny.
Sosban fach yn berwi ar y tân,                A little saucepan is boiling on the fire,
Sosban fawr yn berwi ar y llawr,        A big saucepan is boiling on the floor,
A'r gath wedi sgrapo Joni bach.                And the cat has scratched little Johnny.
Dai bach y sowldiwr,                        Little Dai the soldier,
Dai bach y sowldiwr,                        Little Dai the soldier,
Dai bach y sowldiwr,                        Little Dai the soldier,
A gwt ei grys e mas.                        And his shirt tail is hanging out.
Mae bys Meri-Ann wedi gwella,                Mary-Ann's finger has got better,
A Dafydd y gwas yn ei fedd;                And David the servant is in his grave;
Mae'r baban yn y crud wedi tyfu,        The baby in the cradle has grown up,
A'r gath wedi huno mewn hedd.                And the cat is 'asleep in peace'.
Sosban fach yn berwi ar y tân                A little saucepan is boiling on the fire,
Sosban fawr yn berwi ar y llawr                A big saucepan is boiling on the floor,
A'r gath wedi huno mewn hedd.                And the cat is 'asleep in peace'.
Dai bach y sowldiwr,                        Little Dai the soldier,
Dai bach y sowldiwr,                        Little Dai the soldier,
Dai bach y sowldiwr,                        Little Dai the soldier,
A gwt ei grys e mas.                        And his shirt tail is hanging out.
Aeth hen Fari Jones i Ffair y Caerau        Old Mary Jones went to the fair in Caerau,
I brynu set o lestri de;                To buy a tea set;
Ond mynd i'r ffos aeth Mari gyda'i         But Mary and her teacups ended up in a ditch,
llestri        
Trwy yfed gormod lawer iawn o 'de'        Through the consumption of rather too much "tea".
Sosban fach yn berwi ar y tân                A little saucepan is boiling on the fire,
Sosban fawr yn berwi ar y llawr                A big saucepan is boiling on the floor,
A'r gath wedi huno mewn hedd.                And the cat is 'asleep in peace'.