If you are a British conservative and a supporter of the National Health Service (NHS), i.e. Britain’s form of universal healthcare introduced after WWII, then you’re likely a lot more comfortable with the notion of a welfare state than most American conservatives or libertarians.
And therefore maybe less of a hypocrite on that particular subject.
Well, be that as it may, the decision to raise a child is the most important decision a person will ever make in their lifetimes. Legally, the state imposes responsibility to parents for that child’s wellbeing until the child reaches the age of 18. Morally and emotionally, a parent is attached to that child for their entire life.
And you want to have the state impose that choice and that grave lifelong responsibility upon heterosexually-active people, even if they are trying to avoid getting pregnant and take precautions like birth control that happen to fail.
Well, I have bad news for you. The state can’t possibly regulate what it doesn’t yet know about. And there’s simply no way of ascertaining one’s pregnancy status until, at the very very earliest, 8-10 days after sex if you are peeing on a stick literally every day. Even then, for most accurate results it’s recommended to wait until the start of your next period, which could be up to 28 days or so.
Practically speaking, there is no way for life to “begin at conception” if the state and even the mother don’t know about it yet.