Lord Newby, Liberal Democrat spokesman on the Treasury, has agreed to put forward suggestions from the Unclaimed Assets Charity Coalition when amendments to the bill are debated in the House of Lords this week.
"By far the best way of dealing with dormant accounts is to reunite them with the people they belong to, and more needs to be done by the banking sector to bring that action," Lord Newby said.
"We would also like to be able to extend the definition of unclaimed assets to money held by insurance companies, because the scope of the bill is quite narrow."
Newby added that ministers should rethink their decision to allow the financial sector to surrender assets on a voluntary basis. "If the Government decides these assets should be put to good use, everyone should do it and it should be compulsory," he said.
The coalition will be holding further meetings with peers over the coming weeks and has also written to Treasury minister Kitty Ussher and third sector minister Phil Hope to ask for their support in strengthening the bill.