A “vital” rule change to give two organisations privileges and certain immunities has received backing from MPs.

The Lords had already supported the Commonwealth Parliamentary Association and International Committee of the Red Cross (Status) Bill earlier this year, which would allow the two bodies to act in a way “comparable to that of an international organisation” which the UK has signed up to.

At its second reading on Tuesday, Conservative former minister David Mundell said his delegation was attacked on a visit to South Africa with the Commonwealth Parliamentary Association UK.

He said the assailants allegedly argued Commonwealth Parliamentary Association (CPA) delegates were “neo-colonialists” because the organisation was not an international organisation but instead a UK-based charity, and suggested conversations about the group’s status distracted from British criticism of “the assault on the LGBT community in many Commonwealth countries”.

The CPA is made up of more than 180 law-making bodies around the world, including the UK Parliament, Stormont, Holyrood and the Senedd.

The International Committee of the Red Cross (ICRC) is a neutral organisation which provides assistance for people affected by conflict and natural disasters.

Mr Mundell told the Commons the CPA’s status was “top of the list of issues to be discussed by the speaker of the South African parliament” when he met with representatives, and also that “when the speaker of the Ghanaian parliament visited this country, this was the top issue on their agenda”.

On the attack, he said: “The structure of the international Commonwealth Parliamentary Association was given as one of the reasons as to why we were ‘neo-colonialists’ because the organisation wasn’t a full-standing international organisation, it was an English charity and they used that to further their arguments”.

Mr Mundell continued: “So it’s not just a nice thing to do, it’s a vital thing to do in order to ensure that we can be fully participative and respected in discussions.

“And if we want to raise difficult issues, and there are difficult issues to raise in the Commonwealth, particularly the assault on the LGBT community in many Commonwealth countries – we want to raise those issues – we can’t then be confronted, ‘Well, what are you doing about this issue that’s important to us?'”

Privileges which the CPA and ICRC could receive include immunity from legal process, some tax exemptions and some immunity from import or export restrictions.

The Bill faces further scrutiny in Parliament at a later date.

Foreign Office minister Stephen Doughty said “the UK is deeply committed to the Commonwealth”.

Mr Doughty said the Bill will allow “both organisations to be treated in a manner that is comparable to an international organisation, with associated privileges and immunities”.

He added: “This Bill will give the CPA and the ICRC the correct status in legislation to allow for both organisations to continue their international operations without unnecessary restriction.”

Shadow foreign office minister Alicia Kearns welcomed the Bill and said it will “guarantee for the ICRC that sensitive information it must be able to share with the Government” is protected.