155mm, it's been 35 hours since you posted this; have you grabbed the tape measure yet? Quickest route to a definite response.
Rick da Jawa: Gotta disagree with you. A 590x38 is theoretically the same diameter as a 700x23c. Unless 155mm's bike is from the very early 60s, it is Raleigh buuilt and will easily take a 700x28c, maaaaaaaaaybe squeeze a 700x32c in there; in either case, no fenders--or thin new-style fenders.. This is why the OP should have taken some measurements at about 311mm up the fork blades and stays, to measure how much room there is going up and side-to-side at that point. Raleighs are odd in that they tend to clear more out back then they do up front. Oh, btw, that fork probably takes a scrawny 5/16" axle and is spaced very narrowly, at like 81mm. So, you'll need to modify the fork if you want it to take a modern/common hub. Back is spaced about 115mm, so there's that, too. If you want to swap the fork, you'll need to replace the headset. Even if you find a Raleigh-built fork for 28" wheels, the steerer tube will almost certainly be too short for your frame.
My advice: If the Herc ain't a step thru, flip it as-is for a quick $100 and buy the bike you want. If it's really clean, you might get more. If it's a step-thru, you might get $75...