The survey of 764 businesses collates economic activity data from a range of sectors.
It shows stronger growth in the distribution (retail, wholesale and motor) and consumer services sectors in March, compared with February.
That compensated for a weaker performance in manufacturing, where 11 of the 18 sub-sectors reported slowing growth, and in professional services where firms have been squeezed by stronger competition.
The overall reading of +18% for the three months to March shows that private sector growth was almost unchanged from the three months to February reading of +19%.
Businesses expects this growth to strengthen, driven in particular by a pick-up in professional services, consumer services, and manufacturing.
The balance of expectations for business growth over the next three months is +25%.
That represents an increase on the +18% that was actually recorded in March but represents a significant scaling back of expectations compared with this time last year.
“The outlook for 2015 looks encouraging,” said Katja Hall, CBI deputy director general.
“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.”
“The main risk to the UK economy comes from the Eurozone, with continuing wrangling over Greece’s bailout package stoking uncertainty. Plus, many businesses will also have to contend with a stronger pound weighing down on already weak export growth,” Hall added.
