Bašić said she first began learning the bellows-driven instrument aged nine.
She said: “My roots are that my family are from the former Yugoslavia, from Serbia, where the accordion is the number one instrument and leads the orchestras.
“I’ve always had a passion and a love for it.
“So I actually learnt to play the accordion in this country, did all my grades, etc.
“Then I really wanted to do something that involved others who loved it as much as I do.”
She began teaching others to play with her kitchen “classroom” while she juggled raising children, doing a degree and running a business.
The band has grown from the original five to 38 members and also raises tens of thousands of pounds for charity through its fundraising concerts.
Bašić is now its musical director.
She said: “We all say it’s more than the music, it’s become like an extended family and people look out for one another.
“We have a very active WhatsApp group.
“It’s just brilliant to be part of something that makes people happy.”
The musician said the group would “really like” to win the award which is voted for by the public.
“We want to put the accordion on the national map as an instrument that’s not recognized as much as it should be, that’s where we’re coming from with it.”
The Royal Philharmonic Society is a London-based charity set up in 1813 to celebrate and promote classical music.
Voting for the RPS Inspiration Award is open until 11am on Monday, 2 February.