In a lot of cases, it depends what you class as a field. One of my favourite routes takes a designated footpath along the edge of open moorland onto one of the Peak District’s gritstone edges. We walked this path for years without seeing cattle until one weekend we suddenly seemed to be in among highland cattle who were docile enough, but also several young bullocks of a non highland breed, one of which straddled the path we were walking on. I moved off the path and gave him a wide berth, but he came up behind me and with a nudge, knocked me clean off my feet. I got up and DH came and tried to shoo him away but he wouldn’t be shooed until DH waved his rucksack at him. No fences, no walls, designated and well worn right of way. There should at least have been signage.
I have been walking in the Peak District since I was a child and cattle roaming on moorland never used to be an issue. One of the large National Trust moorland estates regularly run quite large herds, but there are signs all over the place warning you of the dangers, especially if cows have calves in tow, and asking you to avoid them or approach them with care and what to do if you have a dog with you.
As for right to roam, I have been told many times by foreign visitors that we are lucky in this country to have access to so many places to walk freely. There has been something of a crusade recently to encourage people who might not otherwise use the countryside for leisure to do so. Yes, education is needed, but it works both ways.