flying IMC 5nm east of Sheffield without a radar service is not terribly sensible. See those blue chevrons on the chart, extending to 7nm east of Sheffield? That means there's an instrument approach procedure there in uncontrolled airspace. the procedure may extend a good deal further out than 7nm. The idea of putting those on the map is to try to encourage folks like you not to fly through them.
I disagree. If he was flying through the final approach track for the active runway at Sheffield, and was talking to Sheffield Approach, and was passed timely and accurate traffic information regarding traffic making an approach, then I would suggest the system worked perfectly. The blue chevrons are not there to say 'Don't fly here!', rather that it is sensible to be talking to the associated ATC unit if you intend to do so, for obvious reasons.
Radar is not the be all and end all. Granted, procedural ATC has no idea if there is unknown traffic in your area, but they are just as capable of separating you from known traffic as a radar unit is.