Hi Alpha Golf Mike,
I did what you're thinking about doing and went on the OAA modular course.
A lot of people are making a lot of good suggestions but respectfully maybe you should consider flying in the US. Heres my experience:
1) Like you I needed to hour build to meet the P1 requirement of 100 hours before starting the course. Your CPL-ME training will be VFR in Arizona. I think you'll get more out of being familiar with the airspace around Phoenix. Flying in America is a doddle but when you move up from PA28 to PA34 it helps your confidence if you know the territory. The integrated cadets will have a headstart over you here. There are VFR departure and arrival plates you will be using for all your flights. Maybe grab them off the school before you head out there/when you get there so you can use them in your hour building. Thats what I would have done differently looking back.
You do spend 12 hours initially in a PA28 do familarise yourself with the area and approaches but more familiarity helps.
2) Getting used to the scenery in the UK is nice but the CPL-IR element is just that. We get into the aeroplanes, screens go up and come down when you shoot the approach. They go up again then come back down when you're at MDA on finals back at Oxford. You're following your VORs/DMEs/NDBs the whole time as you're always in cloud or have the screens up. There is no extra benefit to VFR in the UK over what you could gain from flying in the US where you will be doing your VFR CPL-ME training.
Sure there is a valid case for radio practice which is is a considerably higher workload in UK vs US but without the IR rating you can't go into the airways/fly IMC and its juggling the radio while flying under the screens and interacting with controllers while flying at twin speed that makes it challenging which you won't be doing on a PPL in the UK
3)
Most importantly, flying in US is cheaper. Its about Gbp 60-80 an hour for C172/PA28 versus the 130-175 in the UK. Fitted GPS (e.g430) seems to be popular in the US too which is a nice reassurance when starting in unfamiliar airspace. BTW: Garmin430 is what the OAA PA34s are equipped with. I did 50 hours in the US. Sure you pay accommodation & food etc but the numbers still work out (and easily for the amount of flying we needed to do) because the air fare is a non-issue being a sunk cost since you need to jet out there to attend your course. You're saving Gbp 100 per flying hour, do 50 hours, and thats Gbp 5,000 - Potentially a significant contribution to your FI course/type rating/travel costs to Africa or elsewhere. There are no landing fees in the US so you can shoot as many approaches as you like and land at international airports (VFR of course) and it is a lot of fun.
I went out there 2 weeks ahead of my course and completed the hours I needed with 2 days spare. The dry weather is reliable around Phoenix/W.USA so you can plan your itinerary. Accommodation is about USD75 a night.
3) Your biggest challenge and reason to be thrifty is not the flying, its getting a job -well, thats been my experience. To give you an idea I have first time ATPL passes, >90% average, first passes CPL-ME & CPL-IR flying exams, and graded "above average standard" for the MCC & JOC. I also have a postgrad degree from a respectable uni in a mathematical based subject. It has been 4 months now and I am still looking for a lucky break.
Am now looking to go into part time flight instructing-fingers crossed that is an option- Part time because It doesn't pay very much if at all so need a regular full time job to support oneself but I was mentally prepared for this before starting. Digressing, the main thing is you need to run a lean ship with your cash because whatever you choose be it flight instructing, type rating, heading out to Africa etc to do SEP/MEP charter work you'll need some money to get out there
so use your pennies wisely.
Just my humble thoughts & experiences. Hope it helps you make a good decision. I can recommend some great places to fly to if you do go to Arizona to hour-build.