I have seen several of these . chopped barrel with ramp front sight and cylinder chambers bored out to 38 special depth in front of the larger 38 S&W chambers. sometimes stamped "not english made" 38 Special as well as with lots of proof stamping. I would suggest using the 38 S&W if you want to shoot it. The .38 special may be safe but it also may split the cases in the oversized 38 S&W part of the chamber.
PS I just read your other post that states that you cannot insert a 38 S&W cartridge. Parker Hale must have sleeved the chambers or replaced the cylinder which is a big improvement from the run of the mill conversions. It is therefore a candidate for using 38 Special rounds of NON +P variety. Jim
Gun Safety is no accident.