Imperial is measure by ID so the 1/2" pipe is 13mm ID but nearly 16mm OD, so the push fit's internal diameter and O-ring is 15mm and therefore too tight for the imperial pipe. So that's a no to pushfit on imperial.
As suggested, compression will usually always fit, use copper olives as they'll give a little when fitting. use the compression fitting to tap the olive on if it's very tight.