A bill introduced by backbench Conservative MP Therese Coffey has completed its Commons stages.
The Wreck Removal Convention Bill will now go the House of Lords.
The Nairobi International Convention for the Removal of Wrecks (ICRW) was adopted by the International Maritime Organisation in May 2007.
Coffey's bill provides measures to enable the United Kingdom to ratify and implement the ICRW in the United Kingdom's domestic law by the insertion of new sections and a Schedule into the Merchant Shipping Act 1995.
"The underlying principle of that convention is that the liability for removing wrecks is placed firmly with the shipowner rather than the British taxpayer," she told the House.
"The wreck removal convention is a new international instrument negotiated by the previous government, and primary legislation is required to implement it.
"I commend this to my hon. Friends because it is not a European competence; the powers of this House are required to initiate this important law."
Transport minister Mike Penning said the bill has the full support of the government and the opposition.
"I hope that it has a quick and safe passage through the Lords, to use another seafaring term," he told the House.
"The key is that we lead on this matter, and we intend to do so. I will speak to other seafaring nations in the next few days and urge them to push forward as fast as possible, as we have done.
"It is not for me to tell them how to do that in their parliaments, but we must get to 10 nations as fast as possible to get ratification and implementation, because it is crucial that the polluter pays.
"We will do the work and clear up, but at the end of the day, the cheque will come from the polluter."
Shadow minister Jim Fitzpatrick congratulated Coffey on bringing the bill through its Commons stages so quickly.
"There are not many members who, in their first year of service in this place, have the chance to introduce a bill, let alone to pilot one through successfully, if hon. Members will forgive the shipping pun," he said.
"She has achieved that, so I commend her and pay tribute to her ability, tenacity and success in getting to this point."
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