Actually your suggestion does work fine with the default-information. I thought this command only existed for the ospf. The network is a bit complicated, unfortunately I can't say much about it, but think of it as connecting sites between them and at one of the sites, e.q. H.Q. there is a different router from an ISP that (or a firewall) that provides internet connectivity. So we as a company do not offer this internet connectivity.
Moreover I have some problems with redistributing the ospf default route into the BGP. it does not seems to work (although I can get away with it with a simple static route),