So all 4 of us turned up and were told the ticket '0' was the winner.

That was not an outcome we expected.
Did we not fill out the application and sign on page pp342, appendix D sub-para 2 or something ?

Hope for a House lottery, but we seem to have got a lemon instead.

Can we re-draw from the applicants that were there, and then bill us the Gil if we accept the win ?

It would be grossly unfair to run it all again in a second open lottery and have to compete with the new folks that were not ready the first time, but decided to try the second lottery.