The Organisation for Economic Cooperation and Development in Paris decides what officially constitutes foreign aid.
Countries are given a ranking according to need, which is meant to ensure the poorest countries take priority.
The latest update from the Department for International Development (DfID) came as an international body signalled it would resist United Kingdom pressure to change its rules so that the assistance can be classed as part of the aid budget.
Under OECD rules, member states can only send foreign aid to countries on a list approved by the World Bank.
More than 60 tonnes of United Kingdom aid has now reached the Caribbean to support the victims of Hurricane Irma.
“What we are working on at the moment is changing the rules at the OECD, but the manifesto set out that if that wasn’t possible we could look at changing the rules here and that remains the case”.
The British government has so far promised 57 million pounds of disaster relief, but the BBC reported it could not use its foreign aid budget to help the British Overseas Territories because they are considered too wealthy for assistance under worldwide aid rules.
The source said: “These are British people in British territories and in times of need we will stand by them, absolutely nothing held us back in getting help to them”.
I have started an online petition to help the victims of Hurricane Irma in the British Overseas Territories.
It hit more than a dozen Caribbean nations and island territories and claimed at least 40 lives.
And a further 60 tonnes of supplies are en route to the British overseas territories in the Caribbean on board HMS Ocean, which – along with other essential items – is carrying 5,000 hygiene kits, 500,000 water purification tablets and 10,000 buckets.
But he denied the UK had been slow to react, as did Mrs May, who said: “The UK response was a speedy one”.
May also announced the government would be increasing the relief fund for British Overseas Territories left devastated by Irma from £12m to £32m.
Mr Johnson said hundreds more troops were being deployed to the region, reaching 1,250 in the coming days.