I believe British English spelling is fine the way it is. As an American I notice the different spellings but I haven't seen anything that inherently doesn't make sense given the language. I do not think there should be any strides to drastically change the English language, I believe it is in a decent form.
Why would it even be considered a debatable question. That term was coined thousands of years ago. I know most languages derive from Latin or Greek,but you have to be kidding me about a phonetic system. Its fine the way it is, your going to push for systematic failure if you even try to implement this system.
British English spelling should not follow a phonetic system. This would be very confusing for the people who are already using the system. It would create a chaotic system for everyone because some people would not want to use it and would use the old system instead of the other one.
British English shouldn't change a bit. Languages naturally evolve and English is one of them. A phonetic system would just be something else to get used to and would be too hard at this point to implement. Perhaps a phonetic system can be better suited for a future system where kids start learning a phonetic alphabet.
I think overall it would very difficult to change such an establish language to a phonetic system, I think many people would refuse to use a new word or spelling for a word that they have said their entire lives and so you would have society split between those using the new system and those using the old one creating a mess.