The probability priced in for a rate cut in August is ~49%, according to the OIS market. Meanwhile, there's roughly 50 bps of rate cuts priced in by year-end. It's definitely a close call and if the BOE doesn't move in August, traders are still expecting them to at least move in September. The odds of that is seen at ~89% currently.
Given the state of play, a notable miss on the inflation numbers later could very well see traders move to price in a move in August instead. But the opposite will also be a consideration if the inflation numbers prove to be much stickier than anticipated. The key numbers to watch will be the core figure and services inflation.