The 19-year-old has just made his acting debut in the BBC soap as Freddie Slater, son of Maureen 'Little Mo' Slater.
Brazier told Good Morning Britain: "She'd be proud. Why wouldn't she be? Anyone who loves and cares about me, all my friends and family, they're all proud and all supportive, so I'm sure - well I know - she'd be the same."
Goody died from cervical cancer aged 27 in 2009, several years after she split from TV presenter Jeff Brazier, father to her sons Bobby and Freddie, then aged just five and four.
Bobby launched a modelling career at the age of 16, appearing on the catwalk for Dolce & Gabbana at Milan Fashion Week in 2020.
Bobby said of playing Freddie: “This is completely different to anything I’ve done before. I’ve never acted before.
“I’ve been thrown in the deep end a bit but I’d like to say I’m swimming.
“There were nerves but everyone made me so comfortable straight away literally from the first scene.”
His character Freddie was last seen in Walford in May 2006 when he and his mother left to start a new life.
His father was Graham Foster, a friend of his mum who raped her. Her refusal to have an abortion led to her split from husband Billy Mitchell.
Bobby said that despite the reputation of the Slater family in Albert Square, he feels comfortable being part of them.
He added: “It feels like home. I feel like a Slater."
Bobby said dad Jeff had not given him any tips on working in TV but added: “He’s happy I’m working consistently and earning and paying rent.”
Jeff, 43, has previously explained why he charges his son rent.
He said: “If the work ethic isn't there, then I would put some things in place in order to encourage that, such as charging Bobby rent.
"That's something I decided to do because I believe in that as a motivational tool for him."
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