Thomas-Symonds said: "Our focus as we move forward must be working together to not only deliver justice to all those impacted, but also to restore trust in the state to people who have been let down too many times."
The compensation scheme is open to those who were infected and also their family members, including parents, children and siblings, who can claim compensation in their own right as someone affected by the scandal.
Under the old rules, family members who died before their own claim was settled would not have received any compensation whatsoever.
That has now been changed so if they die before 31 December 2031 their payment can be passed on through their estate.
The government will also consult on a number of other issues including how the scheme recognises the impact of interferon treatment for hepatitis C which has been linked to severe side effects, and how severe psychological harm is recognised.
Thomas-Symonds said that the changes would cost £1bn on top of the £11.8bn already set aside to pay compensation over the course of this Parliament. An update on the total cost will be made in the next autumn budget.
Andy Evans, the chairman of Tainted Blood, a group which represents 1,600 victims and their families, welcomed the announcement but said that some issues, including the level of compensation for hepatitis victims, had still not been properly addressed.
"The government is clearly listening to us. It's a shame that it took the further involvement of the inquiry for it to take our concerns seriously, but I hope that this statement marks the start of a better working relationship," he said.
"We must now press forward to ensure that this compensation scheme provides real justice, as far as money ever can, for all victims of this scandal."