Sir Edward has denied allegations that he had breached parliamentary rules, insisting that he was not acting in his capacity as an MP in his role as a paid adviser to the firms.
The companies include the China Ocean Shipping Company (Cosco), owned by the Chinese government.
Sir Edward, who is the House of Commons' longest-serving MP and the Father of the House, is also a board member of the Centre for Global Energy Studies, a London-based think-tank that was set up and run by Sheikh Ahmed Zaki Yamani, the former Saudi minister for petroleum and mineral resources.
Sir Edward's close relationship with China is also shown by his role as an adviser on the country for investment funds run by Dresdner Kleinwort Benson and CGU.
In a statement, Sir Edward confirmed that he was being paid by the companies, but said that the payments did not have to be declared because he did not lobby on their behalf, speak or ask questions for them in the House of Commons.
He added that the arrangement had been cleared in 1996 by the then parliamentary commissioner for standards, Sir Gordon Downey.
"Matters which are not connected to Parliament do not need to be declared.
"This is quite straightforward, it has all been cleared by Sir Gordon Downey," Sir Edward said.
But Fraser Kemp, the Labour MP for Houghton and Washington East, said he would be referring the matter to Elizabeth Filkin, the new Parliamentary Commissioner, to investigate whether there has been a breach of rules. "The rules of the House of Commons apply to every member, whether or not he is a former prime minister," he said.
"There have been fanatical claims about probity by Tories over the past few weeks and unless they want to look hypocritical they should share the concern about transparency which is felt by Labour MPs."
Mr Kemp said he was also writing to William Hague, the Conservatives' current leader, urging him for his support.