The Governor of the Bank of England, Mark Carney, admits some people will be put into hardship by the rise in rates by a quarter point to 0.75%.
Carney said the move was a necessity, as not doing so would have a negative impact on a greater number of people.
Asked if the change in the would cause hardship, Carney told ITV News: "Yeah, but what would cause a bigger hardship to a much bigger proportion of the population is if we don't keep inflation under control."
He added: "We've got to a position, collectively, where finally people's pay packets are growing faster than the prices in the shop and the prices online, people are finally starting to get ahead - it's important that we keep that on track."
Video report by ITV News consumer editor Chris Choi
The decision to increase the rate was unanimous, with the Bank of England's Monetary Policy Committee (MPC) members voting 9-0.
The pound made gains versus the euro following the news and was trading higher by nearly 0.3% at 1.128.
The interest rate decision improved sterling's standing versus the US dollar but was still trading lower by around 0.1% at 1.311.
There are fears a 'no deal' Brexit would result in a recession. Carney says the Bank of England is ready for all outcomes of the negotiations with the EU, pointing to the fact the Bank's estimations post-referendum were correct.
"What we said prior to the referendum was that we felt that the pound would go down sharply, we felt inflation rate would go up above target and the economy would slow and that's exactly what's happened," Carney told ITV News.
"A similar set of outcomes can be expected if there's a 'no deal' [Brexit]. What is important for your viewers to know is that: first, from monetary policy perspective, we can react, we can respond, we've shown that we're willing to do that in the past and would do so again.
"It's very important to know that inflation will be kept under control as well, because, after all, inflation hurts the least well off the most.
"The third thing, hugely important, very complicated, our responsibility: the financial sector. We will make sure and we've taken the steps to make sure that our banks are in a position to continue to lend to businesses and households, even in a cliff-edge, disorderly Brexit and we solve a series of quite complicated issues in financial markets."
The hike sees rates reach their highest level since March 2009, when they were slashed from 1% to the emergency low of 0.5% in an effort to contain the fall-out from the financial crisis.
The decision to raise rates will be a blow to some borrowers on variable rate mortgages, but will offer relief to savers who have seen paltry returns on deposits since rates have languished at 0.5% or below since 2009.
The Bank has signalled there would also be further rises to come as policymakers look to bring inflation back to target, although they continued to stress that these would be "gradual" and "limited".
The minutes explained that Brexit is still one of the most important considerations for the bank's rate-setting committee.
The Bank said "during the negotiation period, those economic implications would be influenced significantly by the expectations of households, firms and financial markets about the United Kingdom's eventual economic relationships with the European Union and other countries, and the transition to them.”
ITV News Business and Economics Editor, Joel Hills calls the timing "curious" considering Brexit negotiations are ongoing.
In its quarterly inflation report, the Bank kept its forecast for growth this year unchanged at 1.4%, but increased the outlook for 2019 to 1.8% from the 1.7% previously predicted.
It continued to pencil in growth of 1.7% for 2020.
The Bank said retail sales had surged by 2.1% in the second quarter, boosted by the recent sunny weather.
"Weather effects - both the snow-related disruption in February and March and the unseasonably warm weather and long sunshine hours in May and June - seemed to have accounted for around half of the second quarter rise."
Bank governor Mark Carney said the bank is “well prepared for whatever path the economy takes, including a wide range of potential Brexit outcomes”.
"The committee recognises that the economic outlook could be influenced significantly by the response of households, businesses and financial markets to developments related to the process of EU withdrawal.
“Negotiations are now entering a critical period, with the UK and EU both seeking an agreement by the end of the year.
”Although the range of potential outcomes is wide, what matters for monetary policy is how people react to developments.“