I work in the Life Insurance Industry. Yes, it is normal for them to take your details over the phone, and it is normal to purchase life insurance over the phone. It also seems to be a pretty normal rate, depending, of course, on your age and your health.
Did you provide them with any medical information: your height, weight, if you smoke, etc? If you haven't, they can change the rate based on that information.
Nothing is binding until you sign the documents you get in the post.
By the way, I checked and Bounty is owned by Friends Provident, which is a very reputable company. (No, I don't work for them.)
Their website shows that they are targeting new parents.
I am not sure if you are clear on this, but this is term assurance, which means that if you don't die in 18 years, you don't get anything, and you don't get back any of the money that you've given them.