The survey also revealed that 18% of UK museums have had to close a part or branch of their museum in the last year or will have to do so in 2016.
The Association said the changes were due to cultural spending cuts for local authorities.
More than 40 museums have closed across the UK since 2010.
That number is expected to grow in 2016, following recent announcements that museums in Lancashire, Durham, Dudley and Leicestershire will have to shut.
Nearly half of respondents - 45% - also said they had increased the number of voluntary staff, compared with 32% the previous year.
There has been a 28% cut in cultural spending by local authorities since 2010.
The Museum Association's findings showed that overall public funding to museums decreased by 2% and income from grants and donations fell by 4%.
The further cuts in local authority funding announced in the recent Spending Review mean that cultural spending by local authorities is set to fall further over the next five years.
The government has made a commitment to keep entry to national museums free but this does not cover the vast majority of museums in the UK.
A spokesperson for the government's Department for Culture, Media and Sport told BBC News it was committed to supporting the UK's cultural institutions, which very firmly included museums.
"One of the best investments we can make as a nation is in our extraordinary arts and museums," said the spokesperson.
"That is why this government has protected funding for national museums to ensure they remain free to enter and secured a cash increase to Arts Council England.
"Councils will have almost £200bn to spend on local services - including museums - over the lifetime of this parliament."
Last year however both Brighton Museums and York Art Gallery introduced charges for entry.
Five Lancashire museums are set to close, including two mill museums, Queen Street Mill and Helmshore Mills Textile Museum.
Sarah Hardy is a former member of staff at Helmshore - she is campaigning for more time to find alternative ways of keeping the museum open.
"We lose our heritage, our local heritage but also our national and even international heritage (if Helmshore closes). Lancashire has a rich industrial heritage... if we lose it, then we have lost it forever, these sites are so unique... they can't just be replaced once they've gone."
Financial pressure is also having an impact on museum collections, with 11% of all museums considering selling off items for financial reasons, up from 9% in 2014.
The survey also showed that museums in northern England, Wales and Northern Ireland reported larger year-on-year decreases in public funding than those in the Midlands, southern England and Scotland.
Sharon Heal, director of the Museums Association, said: "Museums that serve local communities deliver real public benefit and there is a danger that whole areas of the country will have these services wiped out if the cuts continue. The MA will continue to advocate for all museums and the life-changing experiences that they can provide."
Lancashire County Councillor Marcus Johnstone, cabinet member for environment, planning and cultural services, said: "I did not come into politics to close museums or any other public service but the government has continually cut the county council's funding and this is the reality of our situation."
However 61% of museums surveyed reported an increase in visitor numbers year-on-year.
And despite the cuts, museums are fighting back with self-generated funding, with retail sales up 6%.
The Museums Association is the largest membership organisation representing museums and galleries in the UK and the people who work for them.
Between September and October 2015, the Museums Association asked museums to provide information regarding changes to their budgets, staffing operations and general service provision.
The survey was answered by 115 museums, representing all types of museum and all areas of the UK.
There are more than 2,500 museums in the UK.
Nearly one in five museums has introduced charging in the last year or will do so this year, according to a survey by the Museum Association.