It's Henry III, but it's not S 1369, because that's Class 5. The obverse legend starts at 12 o'clock, which means it's earlier than that.
The king hasn't got a sceptre, so it's not Class 4, and the moneyer is named, so it's not Class 1. The regnal number is shown as III (not TERCI), so it's Class 3.
There's a colon stop between REX : III, so it's either Class 3a2, 3c, 3d1 or 3d2.
The eyes are complete circles, so it's 3c, 3d1 or 3d2. The beard is pointed, so it's 3d1 or 3d2. The R doesn't appear to have an upturned tail, so it's 3d1:
Henry III Penny, Class 3d1 (1250), Spink 1364A; North 988.