Ali Harbi Ali, 25, denies his murder and will stand trial later this year. He is also charged with preparing acts of terrorism.
Ms Firth, a barrister, paid tribute to Sir David, who she described as a “great man and a great parliamentarian” as she became Parliament’s newest MP.
“Tonight I pay tribute to Sir David Amess who represented this seat for more than 24 years and was a passionate advocate for Southend West,” she said.
“Sir David was a truly exceptional MP, he was a friend to all and he had a huge impact on everyone who lives here.”
Ms Firth praised other parties for not standing to contest the by-election and recognised the former MP’s family.
“For Sir David’s family and his friends tonight will be a sad and painful day and I would like to pay tribute to Lady Amess and their children,” she said.
“We are thinking of you tonight.
“It is inspiring to see politicians coming together from across the political divide to respect a great man and a great parliamentarian.
“It is the honour of my life to represent the people of Southend West and the place where I was born. As your member of Parliament, I will work tirelessly to build on everything he achieved.”