The US position is somewhat different in that at uncontrolled fields, it is usual to call the center on the phone to receive a clearance (with a clearance void time) prior to departure. In this way the situation doesn't occur.
In the case where this is not possible, IFR flights (on IFR Flight plans) must remain outside controlled airspace unless cleared. In the case of class E though, once two way contact has been achieved (defined as an exchange of callsigns) entry is permitted without a specific IFR clearance. VFR flights require no particular formality to enter class E.
If you are filed on an IFR flightplan, and elect to enter Class E claiming to be VFR, this will cause confusion and potential embarassment...
2D