Buildings Insurance

I insure most things myself, not using an insurance company. I make sure I save enough money so that, for example, if someone stole my bicycle I could buy myself a new one. Is this a good idea?

When it comes to my house though, I couldn't afford to have it rebuilt if it was somehow destroyed in an accident. So I insure it with the Halifax. So when can I stop paying my buildings insurance? When I've got enough money to rebuild the house entirely? That'll take ages, can't I stop paying it now?