The average two-year fixed-rate this week hit 2.53%, the highest level since July 2016, according to Moneyfacts.co.uk.
Monetary policymakers maintained the base rate at 0.5% in May, with just two of the nine Monetary Policy Committee (MPC) members voting to increase rates.
However, the bank said rates were likely to increase if the economy grew, in line with markets still expecting a hike to come this year.
And it appears lenders are not moving to drop rates back.
Charlotte Nelson from Moneyfacts.co.uk said: “Despite the Bank of England keeping the base rate on hold this the upward turn in the short-term fixed rates shows no signs of stopping.
“This goes to show that borrowers do not need to see a base rate rise for rates to rise.
“This upward turn in fixed rates has not affected all of the market however, with the average five-year fixed rate remaining static at 2.91% for two consecutive months.”
BoE could raise rates in August
Earlier this year policymakers had hinted that rates could rise sooner and faster than markets were expecting.
Lenders responded by gradually increasing rates in the weeks leading up to the May rate announcement.
However, the bank opted to hold rates, following a spate of disappointing economic data, but could act again in August if it appears growth is buoyant.
The performance of the economy will now be closely monitored for clues on whether the MPC will hike sooner or later.
Four rises in 18 months
Jonathan Loynes, chief economist at Capital Economics, said: “The bout of softer-than-expected inflation and activity data which caused the MPC to step back from hiking Bank Rate in May is certainly reason for caution.
“But like the MPC, we think that temporary factors were behind the slowdown, and suspect that growth will bounce back in Q2.
“If we are right in thinking that growth will surprise on the upside over the rest of the year, interest rates would surely rise by more than the very modest tightening – of just one hike this year and next – that is currently priced into financial markets.
“Indeed, we expect two hikes this year, and a further two in 2019, taking Bank Rate to 1.5%.”