The mum-of-three also went to the infant school herself and said: 'I'm a passionate England fan, our whole family are, and I remember Gareth from the days he used to play with the Neville brothers and David Beckham.
"Football's coming home.I couldn't listen to it for 20 years, frankly", Southgate said.
'To be able to say I was there on his first day of school is unbelievable.
Southgate's England take on Croatia in the semi-final in Moscow, having beaten Sweden 2-0 in the last eight in Samara.
"It has a slightly different feel for me, but it's nice to hear people enjoying it again".
He said: "I just picked up on what everyone has been saying about Southgate's get-up".
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Schoolchildren donned waistcoats in honour of Gareth Southgate as they prepared to watch England's World Cup semi-final match against Croatia. "It is an anthem and has followed the team for a long time, but involved some hard moments as well".
However the rest of the tournament plays out, Southgate's contribution will be lauded for decades to come and he's come a long way since being described as a safe option after the nightmare which was Allardyce's tenure.
Zlatko Dalic's side go into Wednesday's World Cup semi-final knowing they have to improve after battling through two penalty shoot-outs in the knockout stages in Russian Federation.
Children and adults alike scoured charity shops or created their own garments for "Waistcoat Wednesday", in imitation of the sartorial style of Gareth Southgate, the England manager.
Meanwhile, Three Lions is set to score a UK No.1 this week, 22 years on from when it was originally released.