When do you go "all in" on a contract offer?

[NickFitz]

I have a contract due to start 5th April…

Better get a move on, you're late for your first day

[Tasslehoff]

I have a contract due to start 5th May and obviously as my CV is “out there” I am getting quite a lot of interest. I am committed to my new contract but conscious that it’s never a done deal until your feet are under the table with a signed contract on day one.

I reason I ask, is I have an interview next Tuesday which was set up before I accepted this new contract. I am also still answering the phone and entertaining any decent query’s. Based on your experience when do you guys go “all in” and stop answering the phone/emails and cull all of your previous “leads”. Day one? If so, how do you approach those conversations with the agents? Or once you have accepted an offer are all bets off?

EDIT : Wrong date doh