The Bank of England will raise its key interest rate to 0.75% in May, nearly all the 76 economists polled by Reuters have said.
The economists said the Bank of England will then add another 25 basis points just before Britain is due to leave the European Union early next year.
Soon after the June 2016 vote to split from the EU, the Bank of England cut 25 basis points from borrowing costs, taking them to a record low of 0.25%.
It reversed this move in November, a decision most economists said at the time was a policy error.
All but seven of the 76 economists polled between April 10-17 said the bank rate would go up from 0.5% on May 10 when the Bank of England is also due to publish its quarterly inflation report.
A majority of economists, 37 of 62, said the Bank of England will have lifted Bank Rate to 1% or higher by the end of the first quarter next year.
The median forecast shows the rate at a still historically low 1.25% in the final months of 2019.
UK growth has continued since the referendum, and while Britain has fallen from the top to the bottom of the fastest-growing economies among its peers, the poll forecast only a median 10% chance of a recession this year.
UK unemployment fell to its lowest since 1975 in the three months to February, official data showed earlier this week, although wage growth in the period was not as strong as expected.
But the Bank of England has said falling unemployment should start to push up pay more quickly, the main reason it gave for being likely to raise interest rates faster than it had previously thought.
Progress has been made on a transition period after Britain is due to leave the EU by the end of March 2019, where much of its relationship will remain the same. But a lot remains to be discussed about future trading arrangements.
Economists gave a relatively low 20% chance of a disorderly Brexit, in which no deal is agreed by the end of March 2019. That probability has been the same all year.
In the aftermath of the EU referendum vote to leave, sterling slumped, making imports more expensive and causing prices to rise faster than the 2 % annual rate the Bank of England targets.
But the pound soared to its highest level since then yesterday, reflecting weakness in the US dollar, but also because of seasonal dividend payments to British shareholders from foreign companies.
Inflation is expected to ease and average 2.5% this year and then fall to 2.1% in the following two years, unchanged from last month's poll. Wage rises are expected to outpace inflation this year and next.
UK growth forecasts were also unchanged, with expectations for 1.5% in 2018 and 2019, little different from IMF forecasts published this week.
After a sluggish 0.3% growth expected in the first quarter of the year, median forecasts showed 0.4% up to the end of next year.
Euro zone growth was predicted at 0.4-0.6% per quarter over the same period, but economists in a sister poll cautioned growth would take a further hit from the trade disputes between the USs and China.
Over 90% of respondents said the dispute would also damage UK growth, including two who expected the impact to be significant, but many said Brexit negotiations would hold more sway.
Only two said Britain would benefit.