Bank of England Governor Andrew Bailey told CNBC Tuesday that "the path of interest rates will continue to be gradually downwards," as the central bank juggles taming inflation and stoking elusive economic growth.

"I haven't changed my mind on that," he told CNBC's Annette Weisbach in Sintra, Portugal, where the European Central Bank is holding a forum. "But in terms of where are we going to go in the next meeting? Well, we'll see."

Economists expect policymakers will cut rates by 25 basis points at their next gathering in August, which would take the central bank's base rate from 4.25% to 4%.

But BOE's Bailey told CNBC that policymakers needed to gauge whether persistent inflationary pressures, such as averages wage outpacing inflation and higher energy prices, would continue to soften.

"For me, the key question is, is that softening that we're beginning to see going to come through and create the context where inflation will come back down to target?" he cautioned.

The BOE has a 2% inflation target, but price rises have stubbornly exceeded that level, landing at 3.4% in May — well above the neighboring euro zone's latest inflation print of 2% in June. Growth meanwhile remains elusive, with the U.K. economy shrinking sharply in April as global trade tariffs and new domestic tax rises kicked in.

U.K. Finance Minister Rachel Reeves — who last fall introduced tax increases on businesses to largely fund a mammoth public spending program — said the latest growth data was "clearly disappointing."

She also responded to the May inflation reading by insisting that the Treasury had taken "the necessary choices to stabilise the public finances and get inflation under control," referencing her "fiscal rules" that dictate that day-to-day government spending won't be funded by borrowing.

In the time since those "non-negotiable" rules were set last October, however, the U.K.'s economic and fiscal outlook has become more challenging, with higher debt interest payments and weaker-than-expected tax receipts converging with lower economic growth forecasts. Back in March, the independent Office for Budget Responsibility said that it expects the U.K. to record 1% growth this year and 1.9% in 2026.

Chancellor Reeves has acknowledged that there is "more to do" as the government desperately seeks to boost growth in the U.K. economy.

In order to achieve that while sticking to her fiscal rules, Reeves has essentially been left with three options: cut public spending, increase borrowing or raise taxes further.

Economists say the latter choice is the government's only real option, as it has already committed to higher public spending and a more sustainable borrowing framework.

Central bank policymakers tend to steer clear from commenting on governments' fiscal policies to avoid accusations of interference or bias. Bailey nevertheless on Tuesday told CNBC that, while it was important that Reeves had "set out a very clear fiscal framework," there should be a "suitable amount of flexibility in that."

"The U.K. has got a fiscal framework that the chancellor and I discuss it often. I know the chancellor is very committed to having a robust fiscal policy in place, and that is important as a backdrop to macroeconomic stability," he said.