MPs have rejected attempts to explicitly guarantee that controversial new legislation will not protect British troops from investigations into torture allegations.

Conservative former Cabinet minister David Davis and the SNP both failed in their bids to exclude torture from the remit of the Overseas Operations (Service Personnel and Veterans) Bill.

The Government believes the new legislation will ensure service personnel will be protected from “vexatious claims and endless investigations”, and insist it does not decriminalise torture.

The Bill seeks to limit false and historical allegations arising from overseas operations by introducing a statutory presumption against prosecution, making it exceptional for personnel to be prosecuted five years or more after an incident.

To override the presumption, the consent of the Attorney General will be required, and the prosecutor must weigh up the “adverse impact of overseas operations on service personnel” and, where there has been no compelling new evidence, the public interest in cases coming to a “timely conclusion”.

But campaigners and some senior military figures have warned the legislation will create a presumption against prosecution of torture and other serious crimes, except rape and sexual violence.

An SNP amendment, which aimed to exclude the prosecution of serious international crimes such as torture and genocide from the limitations imposed by the Bill, was defeated by 262 votes to 335 – majority 73.

Mr Davis’s amendment to ensure the Bill’s provisions to block prosecutions would not apply to torture was defeated by 269 votes to 334 – majority 65.

Conservative colleague Anne Marie Morris (Newton Abbott) joined Mr Davis in rebelling to support the amendment but to no avail.

Speaking during the Bill’s report stage, Labour MP Sarah Owen (Luton North) said: “How can this Government call out other states for their use of torture and human rights abuses when they seek to pass legislation which legitimises the very same?”

Labour MP Olivia Blake (Sheffield Hallam) said: “There is no stopwatch on justice and there are no exceptions, no ifs, no buts on torture or human rights and that’s why I’ll be joining colleagues in supporting these amendments this evening in voting against this Bill.”

But defence minister Johnny Mercer said the Bill “does not decriminalise torture”.

He argued: “I am very much aware that many people have misinterpreted the decision to only exclude sexual offences from the presumption against prosecution, including suggesting that it somehow undermines the UK’s continuing commitment to upholding international human rights law and humanitarian law – including the UN Convention against Torture.

“This, as my honourable friends well know, is completely untrue.

“The UK does not participate in, solicit, encourage or condone the use of torture for any purpose and we remain committed to maintaining our leading role in the promotion and protection of human rights, democracy and the rule of law.

“The Bill does not decriminalise torture or war crimes and it will not encourage or allow our service personnel to act with impunity.

“We will continue to take other offences such as war crimes and torture extremely seriously. The severity and the circumstances in which it was committed will always be factored in the prosecutor’s considerations.”

Speaking at third reading, Defence Secretary Ben Wallace added: “There have been many inaccurate and wild accusations about the measures in this Bill.

“It does not prevent armed forces personnel from being prosecuted for crimes they may have committed. It does not remove prosecutors’ independence or ability to prosecute on the basis of any new or compelling evidence for any crime at any time.

“It does not undermine the UK’s adherence to the UN Convention against Torture, commitment to international law or willingness to investigate and prosecute any alleged criminal offences.”

For Labour, shadow defence secretary John Healey said the UK can do “so much better” than the legislation as it currently stands.

He told MPs: “I think we all want the same thing – Labour, the Government, the public, the armed forces. We all want to protect British troops and British values and this should not be a matter of party politics.

“And it is simply wrong to make debate on this Bill divisive or to brand those who challenge ministers on the content of this Bill as somehow standing against British troops.”

The Bill later cleared the Commons after MPs gave it a third reading by 345 votes to 260, majority 85. It will undergo further scrutiny at a later date.