A new report from Lord Darzi says hundreds of children in London take up smoking every week and that the city should lead the way with these bans, which could become a blueprint for the rest of Britain.
The peer believes more needs to be done to help people quit and to discourage kids from taking up the habit.
Lord Darzi said: "We know the number of kids taking up smoking, and that's probably the biggest challenge is, how do we stop kids taking it up? Nicotine is highly addictive, we know that, and we need to help and certainly create an environment in which healthier choices are taken up easier."
Some critics of the idea think there is not enough evidence that a ban would save lives.
Dr Laurence Crutchlow from the Christian Medical Fellowship agrees that something must be done, but he isn't sure Lord Darzi's approach is the right one.
On Premier's News Hour, he said: "We still have a significant problem [but] rates are lower than they used to be. In London, I think just under one in five of the population smokes now. That's down from where it was, but of those people, probably one in two of them will die early because of their smoking if they carry on doing it."
However, Dr Sean Gabb, the Christian director of Libertarian Alliance, thinks it is not the government's job to stop people smoking.
On the News Hour, he said: "It is not the business of the state to tell us how to live. It is the business of the state to stop us from robbing and murdering each other; everything else is down to our own compact with God. This is a question of the state stepping into God's shoes."
Dr Laurence Crutchlow, Christian Medical Fellowship:
Dr Sean Gabb, Christian director of Libertarian Alliance: