Christians Against Poverty said an increase in the jobless number by 15,000 showed the country should always be thinking about those unable to get work.
The Office for National Statistics said the unemployment figure had gone up for the first time in more than two years and now stands at 1.85 million.
It said the increase was the first quarterly jump in the number since the three months to March 2013.
ONS statistician Nick Palmer said: "It's possible that the rate of improvement in the labour market that we have seen over the last three years may have eased off, though it is too early to be certain."
James Carne from Christians Against Poverty's job clubs told Premier it was concerning.
He said: "The concern is always actually what's going on for individuals.
"So we're still seeing, whether it's up or down, over 1.8 million people unemployed at the moment, so we need to be concerned about any time unemployment starts to rise.
"We always need to be considering the individuals and the impact that is going to have on them - being unemployed."
He added that churches had a responsibility to help people looking for work and said CAP's job clubs could offer support to Christians who were finding it hard to get a job.
But the figures also showed that pay rises continued to accelerate, with average weekly earnings up by 3.2% year-on-year in the three months to May, up from 2.7% in the three months to April.
It is the strongest rate since April 2010 and with inflation hovering at around zero, it means that real terms pay is improving at a rate not seen for nearly eight years.
Regular pay excluding bonuses rose by 2.8%, the highest rate since February 2009.
Employment Minister Priti Patel said: "The strength of the UK labour market is something we should take great pride in.
"Today's figures show real wages growing at the fastest rate since 2007, and near record numbers of women in work.
"As part of our one nation government, we want everyone to succeed and achieve their full potential.
"With the Government's new productivity plan, and introduction of the new living wage, we are ensuring everyone benefits from the economic recovery."
Premier's Antony Bushfield speaking to James Carne from Christians Against Poverty's job clubs: