It is possible to get your licence on an LAA machine and save a lot of cash but it is complex if you are new to GA.
You need a suitable aircraft, a Jodel 112 could work in this case at a cost around £10,000. This is a two seat aircraft and was the standard French flying school trainer in the 60’s/70’s/80’s. To do this you need a good inspector and you need to learn to do your own maintenance under his supervision.
You need an instructor who will teach on the aircraft
You need a place to base it which works for the instructor.
Put that together and you can get a licence and hour build for very little cash. At the end of the exercise, provided you have looked after the aircraft you will get about the same money back as you paid. Risk is something goes bang and costs you £15k to fix, but if you know what you are doing / have a good inspector this is unlikely.
There was a study done comparing the safety record of LAA aircraft v C of A types over 20 years that showed no difference in safety. There are bad LAA aircraft and bad C of A ones; all comes back to a really good inspector. I have owned a verity of LAA machines ranging from a 1946 C120 to a state of the art MCR01 which I built from a kit 8 years ago and have just toured France in for a week.
Rod1