Business lobby group, the Confederation of British Industry (CBI), estimated that the UK's economy expanded by 0.7% in the three months to March, up from 0.6% in the previous quarter. It also said growth would probably gather some momentum in the current quarter.
The main risk to the UK economy was related to ongoing eurozone worries and Greece's bailout package, it said.
CBI's monthly survey includes 764 private firms from a range of sectors.
It said businesses in the UK would also need to cope with a stronger pound, which was already weighing down weak export growth.
The lobby group's monthly private sector growth indicator showed an overall reading of 18% for the three months to March which was "almost unchanged from the three months to February (19%)".
The percentage reading indicates the number of firms reporting that business performance was up, compared to those reporting it was down.
The survey showed firms expect growth to strengthen in the coming months, with a pick up in business and consumer services, together with the manufacturing sector.
"The outlook for 2015 looks encouraging," said CBI's deputy director general Katja Hall.
"Our surveys show it's been a solid start to the year with the prospect of stronger growth to come.
"The benefits of lower oil prices should be increasingly felt; with cheaper petrol boosting households' incomes and spending power, and cutting costs for many businesses," she said.