No, you don't need permission. A handful are "closed" on "safety" reasons of tottering headstones.
I would suggest you take it a bit further, have a good wander round the church, too. You may find all sorts of interesting things - memorial plaques and stained glass, war memorials, lists of churchwardens, and to my joy in one church I visited recently, a map of the churchyard identifying the graves! You may also find typescript lists of baptisms, marriages and burials. And just soak up the place - this is where those great milestone events of people's lives were celebrated.
Worth trying to find details on the web first - sadly many churches are kept locked and if you want to visit inside the church, you may need to make arrangements to borrow the key: this is even more likely with churches that are barely used. Sometimes you'll need to go to the vicarage, sometimes the corner shop, sometimes the churchwarden: and a phone call in advance will help!
