Harriet Harman, the constitutional affairs minister, last week unveiled plans that would allow bereaved relatives to make personal statements in court after the conviction of a killer, and before sentence is passed.
However, the trust said that the ideas outlined in a paper from the Department for Constitutional Affairs needed to be extended.
"It doesn't go far enough," said Clive Elliot, director of the trust and vice-chair of Victims' Voice. "What we need is legal representation throughout the trial."
The trust points out that the International Criminal Court has already moved to give victims' relatives legal representation at each stage of the court process, and urges the British criminal justice system to follow suit.
Victim Support - which is due to publish its own research later this year on the effects of homicide on victims' families - has taken a more cautious approach. It warns that the existing plans would need to be managed carefully.
Findings from the charity's research show that responses vary from family to family. Although some relatives would welcome the chance to put their views across, others might shy away from such a daunting prospect, it has found.
Despite the Government's suggestion that a family's verbal statement would have no effect on the final sentence, Victim Support has recommended cautious management to ensure all families' interests are taken into account.
The DCA paper is currently the subject of a three-month consultation.