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One Britain One Nation (OBON) Day wants schools across the UK this Friday to sing the “patriotic song”, after the campaign was founded by retired police inspector Kash Singh.
However, the campaign, and the song, have both come under criticism – even from one Westminster Tory.
Mr Singh said the concept was "born from my dream as a police officer" after coming to the UK as a six-year-old boy who "couldn't speak a word of English".
He said he set up the campaign in Bradford, West Yorkshire, in 2013 after retiring from the police force in 2012.
The UK’s Department for Education (DfE) said it is encouraging schools across the UK to celebrate OBON Day on Friday, so "children can learn about our shared values of kindness, pride and respect".
Ms Sturgeon, Speaking after meeting with EU citizens living in Scotland and organisations supporting people to apply for settled status to remain in the UK, she said: "I'm trying to imagine the outrage there would be if the Scottish Government was insisting or even encouraging Scottish school kids to sing some song about how great Scotland is.
"People would be - and rightly so - up in arms about it.
"It's ludicrous and it perhaps says everything about the disinterest the UK Government has in Scotland that they're asking this to happen on the day Scottish schools go off on their holiday.
"Every aspect of it is ludicrous and I think it says sadly so much that we know about the misguided priorities, the hypocrisy and just the ridiculous nature of a lot of what this UK Government is doing.
"Meanwhile, EU citizens that have been here for most of their lives and are working so hard to help make the country what it is are having to jump through hoops to stay here."
But No 10 said the DfE had not asked anyone to sing songs.
The Prime Minister's official spokesman said: "The Prime Minister supports schools promoting fundamental British values, including tolerance and respect, and we endorse One Britain One Nation's aims to help children learn about equality, kindness, pride, but I will point out the department has not asked people to sing songs or promoting any specific materials for One Britain One Nation day."
The idea has been derided by one of the Conservative Party's own MPs, Caroline Nokes.
The MP for Romsey and Southampton North retweeted a preview of the OBON song saying: "I can't unhear this (however fervently I wish I could)."
The OBON website describes its vision as to "create a strong, fair, harmonious and a proud British Nation, celebrating patriotism and respect for all our people".
Downing Street said the celebration date had been chosen by OBON, not the UK Government.