But Cumbria Chamber of Commerce struck a note of caution.
It said it was disappointed that the base rate had risen but was relieved the rise was only a quarter point.
Rob Johnston, chief executive, said: “We believe the increase is premature. “It isn’t needed to keep a lid on inflation, because inflation is falling already, and it will make it more expensive for businesses to borrow and invest.
“It’s another cost for businesses to bear on top of the increases in business rates, auto-enrolment pension contributions and the National Living Wage, and it will weaken consumer demand in the wider economy.
“That said, it is only a quarter-point rise when some commentators had been forecasting a half-point increase.
"We urged caution on interest rates when Sir Jon Cunliffe, one of the Bank’s deputy governors, addressed a chamber lunch in Kendal last month.
“He appeared receptive to our arguments but my guess is that the Monetary Policy Committee felt that they had to increase the base rate to give them headroom to cut it again to stimulate the economy if there is a difficult Brexit.”
Minutes of the Bank's rate meeting 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".
Armstrong Watson is holding a free business briefing with the Bank's agent for the North East on Wednesday, August 8, at Carlisle Racecourse.
Steve McCullough, business development and marketing director with Armstrong Watson, said: "This is the second year we have been asked to host this event for the Bank of England and it is a coup.
"It's a great opportunity for businesses of all shapes and sizes to meet the Bank of England representatives and find out more about the inflation report.
"It's a direct link to the Bank of England and will allow business people to hear exactly what it is thinking."