Four stone overweight you say? Sounds very like me.
There are two immediately obvious differences.
1. You are in North Derbyshire and I'm in Essex. 45 miles in the respective counties are very different propositions.
2. Even given the terrain difference, you are keeping up 15mph. Last year, my moving average was something like 9.5 mph. OK, we tend to do heavily-laden tandem tours and that brings it down, but even so, on my solo machine I reckon 11 mph is a good enough average.
I can keep going for a very long time if I need to. I haven't done any very long rides this year. I've done a few over 60 miles, and quite a lot over 50, but I've not had that much trouble. I always try to make sure that rides include pubs and tea rooms.
I'm 56 and arthritic. These two factors definitely contribute to my lack of speed, but as has been observed above, I probably benefit through extra stamina as a result.
I'm afraid that, although cycling gets you to a pretty good level of general fitness, you won't lose a lot of weight as a result. We just did a 550 mile tandem tour and I was about 1.5kg heavier after I got back. Full cooked breakfast (we were in B & Bs) as well as a big pub meal every night saw to that, but I bet my muscle mass had increased.