The Confederation of British Industry (CBI) estimated that Britain's economy expanded by 0.7% in the three months to March, up from 0.6% in the previous quarter.
Business lobby group also said growth would probably intensify in the current quarter.
"The outlook for 2015 looks encouraging," said CBI's deputy director general Katja Hall.
The ongoing eurozone worries and Greece's bailout package bear the main risks to the UK economy, says the group.
CBI's monthly survey includes 764 private firms from a range of sectors.
According to the poll, UK businesses would also need to cope with a stronger pound, which was already weighing down weak export growth.
The group's private sector growth indicator signalled 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 amount 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 ramp up in business and consumer services, together with the manufacturing sector.
According to Katja Hall, the group's chief, their 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.
