RFA Mounts Bay and its crew working in the Bahamas following Hurricane Dorian have "made a material difference to the lives of thousands of people".
Speaking to Forces News, the UK's Defence Attaché to the Caribbean made the estimate and praised military personnel deployed to the region who are "working to the extreme parameters" of their endurance.
Personnel from the Royal Navy and British Army are continuing to assist with the relief effort following the hurricane.
They have been delivering water, shelter kits and medical care, as well as evacuating casualties.
"Mounts Bay has made a material difference to the lives of thousands of people - whether it be through getting critical aid to them, or evacuating them if they are injured or indeed delivering medical care to them," Lieutenant Colonel Anton Gash said.
"The challenge [personnel have] had has been constant operations, really.
"They’re working around the clock, they are working to the extreme parameters of probably endurance, beyond what they were designed to do.
"Because everybody on board understands the criticality of the situation that people are genuinely suffering, and everybody is clearly prepared to go the extra mile and more."
At least 43 people have been killed in the Bahamas with thousands more being evacuated, including a British citizen who was rescued by UK military personnel on Wednesday.
RFA Mounts Bay, which is leading Britain's response, has been in the region since June preparing for hurricane season and began landing personnel and emergency relief in the Bahamas last week.
The Ministry of Defence has bolstered Britain's military response to the hurricane with the arrival of an extra 18 medics at the weekend.
A UK operational liaison and reconnaissance team are also now in the capital city of Nassau.
British personnel are working alongside civilians, as well as militaries from across the world including the US, Canada, the Netherlands and the Cayman Islands.
"Mounts Bay as you know has been here for a considerable amount of time, she was the first real international response on the scene," said Lt Col Gash.
"She’s been getting through to isolated communities who really haven’t been identified before, getting through to them, delivering that aid, and now her onboard engineers are working on clearing routes so that the isolated communities can reconnect to the areas that they haven’t been able to get to."
RFA Mounts Bay will soon be joined by Royal Navy ship HMS Protector.
The ice patrol ship is currently in Bermuda, taking onboard supplies including food, water and clothing.
Extra medics and equipment will also join up with Mounts Bay.
"We’re looking at both evolving weather patterns and anything else that might be coming in and as our understanding of the situation on the ground evolves we can better target where we’re putting our aid," Lt Col Gash continued.
"We’ve moved, for example, Mounts Bay several times. Subtle movements once we identify areas of particular vulnerability, we’ll obviously task her helicopter and the Cayman Islands helicopter to go where the point of need is.
"For example, the initial focus what quite rightly search and rescue and bringing out the critically injured – we now have the ability to look slightly more widely than that at isolated communities, people who perhaps aren’t injured, but if they aren’t helped quickly they then move into an ‘at risk’ category.
"It's building our understanding, it’s continuing to deliver vital relief on the ground but also starting to do work that supports the wider recovery effort.
"Helping with both assessments and analysis and practical activity when we can, to reopen ports, reopen airports, to use our engineers to clear blocked roads and routes, to do repairs on bridges and culverts.
"What this is all about is restoration of normal life, that’s what the people of the Bahamas want."