From what I've been seeing thanks to kellylen's links, I'd say this is most definitely BPO Code, British Post Office.
Example of BPO Code:
Code on Bree's medical chart:
BPO 4 State Code (British Post Office, Royal Mail Code)
BPO (British Post Office) 4 State Code is a new postal bar code symbology that has been developed by the British Post office for encoding European postcode data similar to the way the U.S. PostNET symbology is used for encoding Zip Code data. At the time of this writing, the BPO 4 State Code has not been officially adopted as the standard for European postal applications however it is anticipated that it will be sanctioned sometime in 1995. The goal of BPO 4 State Code is to provide European countries with a simple and efficient postal bar coding scheme.
The U.S. PostNET symbology encodes numeric characters in a pattern of four bars per character with each bar being either tall or short (i.e. two possible "states" for each bar). The U.S. technique thus allows for up to 16 different possible bar patterns for each set of four bars and is adequate for encoding the ten digits zero through nine. Because European postcodes contain both alpha and numeric characters, (thus requiring a minimum of 36 different possible patterns for the characters A-Z and 0 to 9), each character in the BPO 4 State Code is encoded into four bars with each bar having four possible "states". The four states are: tall bars, short bars, medium height bars extended up from the middle of the symbol and medium height bars extended down from the middle of the symbol. In theory, the BPO 4 State Code is capable of encoding up to 128 different characters however only the characters A through Z and 0 to 9 have been assigned unique bar patterns.
BPO 4 State Code is a fixed dimension symbology meaning that the height, width and spacing of all bars must fit within exact tolerances.
Now, all we have to do is figure out how to read the states within the code.