Bank of England governor Mervyn King must now write to new chancellor George Osborne to explain why the cost of living – set out in the consumer prices index (CPI) – is more than a percentage point above the target of two per cent.
Rising fuel costs and the tax rises on alcohol in March's budget have contributed to the jump.
The figure represents a 17-month high.
Economists had expected only a slim rise from 3.4 per cent in March to 3.5 per cent in April.
The retail prices index, which includes mortgage payments, was 5.3 per cent – up from 4.4 per cent.
Howard Archer of Global Insight said: "It should be noted that inflation was distorted upwards by the tax increases in the budget being largely passed on in April this year, as opposed to May in 2009.
"We believe that April's consumer price inflation rate of 3.7 per cent should mark the peak.
"Inflation is expected to start heading down in the near term as temporary upward pressures start to unwind."