FREETOWN (Reuters) - Britain said on Tuesday it would not be seeking U.S. military assistance to fight Ebola in Sierra Leone where it expects to see "enormous change" by the end of January following a surge in response measures.

As a U.S. operation of 3,000 troops begins to turn the tide against the deadly virus in neighboring Liberia, calls have grown for it to shift resources towards ally Britain, which is leading the response in Sierra Leone.

Rates of infection are rising fastest in the former British colony which has more than half the 18,000 confirmed cases of Ebola reported since the virus first emerged a year ago from the Guinean forest.

Speaking on the eve of the month-long surge in and around the capital Freetown announced by the government earlier this week, the head of the British taskforce Donal Brown said he expected a breakthrough within four to six weeks.

"The pieces are in place to fight the disease, which weren't here a month ago. So I think you will see enormous change in the next few weeks," he told Reuters at the command and control center for the Freetown area on Tuesday.

Under the government's plan, health workers will go house to house seeking out Ebola victims and anyone with whom they've had contact, transporting those infected with the virus to new British-built treatment centers.

While Britain is discussing how the U.S. government might provide more foreign health workers and assist in the building of additional laboratories for Ebola testing, Brown said there was no need for U.S. military support in Sierra Leone.

"What Sierra Leone still needs is very specific niche support," he said.

The British military has nearly 800 soldiers in Sierra Leone and has opened six Ebola treatment centers since early November, although Sierra Leone's government has complained this is too slow.

Britain plans to intensify its Ebola response in the area around the run-down capital Freetown, which accounts for around half of national cases. But beating the virus in the long-term will depend on the ability to stamp out rural outbreaks.

The UK is calling for additional resources from the World Health Organization to boost case surveillance for rural areas, Brown said.

"I think you will see sporadic outbreaks and we want to make sure we can run towards them and clamp down," said Justine Greening, Britain's International Development Secretary who is visiting Freetown this week.

(Reporting by Emma Farge; Editing by Joe Bavier and Ralph Boulton)