"an unprecedented increase" is correct and usable in written English.
You can use it when referring to a sharp rise or jump in a particular amount or number. For example: "The sweltering summer temperatures led to an unprecedented increase in energy consumption."
Job losses and cutbacks have produced an unprecedented increase in the uninsured.
The last decade has seen an unprecedented increase in scientific publications and policy development on overfishing.
The 19th century also saw an unprecedented increase in travel and in cross-cultural influences.
Last year, there was an unprecedented increase in the number of suicide attacks, according to the Interior Ministry.
"They may not be homophobes, but they are the source of an unprecedented increase in homophobic incidents recorded by SOS Homophobie," the group's report on 2012 states.
Cancer Research UK, which did not start the campaign, said the #nomakeupselfie trend had resulted in an unprecedented increase in donations.
"We are witnessing an increase in the scope of human rights violations in general, and an unprecedented increase in the number of civilian casualties," the group said.
"The last few months have seen an unprecedented increase in violence against human rights and minority rights activists in Pakistan," the group's said in a statement.
No wonder then that the UK is one of only four countries in recent years where there has been an unprecedented increase in material deprivation among children.
The crisis coincided with an unprecedented increase in the number of free schools - run by teachers, parents, faiths groups and private sponsors - with 93 opening this term.
"On the contrary, we abhor these acts and are doing everything we can to bring the number down as low as possible," he said, citing an unprecedented increase in prosecutions of union killings in the past year.
