This is a good question and one every pastor should consider. My dear friend, Jeremy Walker, has written two really helpful pieces on this topic of street preaching, specifically who should engage and how to do so. I know of no one better to address this issue as Jeremy is a passionate street preacher, going weekly to the dark streets south of London to preach to whoever will stop and listen. He is also a very faithful pastor with deep convictions for soul care.
If you think it would be a challenge to preach in the streets in America, I would argue it is more so in the UK. Pastors, read these two articles Jeremy wrote. They will help you begin to evaluate these issues for your church members and even yourself. Guessing and gauging the street preaching Thoughts on street preaching