In the 1960's, home birth was normal and breech wasn't considered reason for a mother to give birth in hospital - let alone a reason to have a CS!
In the 1990's most breech's were in hospital, but so were most births - but breech was still within the domain of "normal" and handled by MWs
In 2000, Hannah et al published a paper in The Lancet colloquially known as the "Term Breech Trial". This was a large, randomised controlled, multi-centre study that tried to look at the safety of breech delivery c/w CS. They found that CS was much safer. In consequence, the vaginal breech rate in most western countries cratered and CS become common place.
Since then the Hannah study has been widely discredited (that's a whole other thread in itself - but there were major flaws with the planning, the execution and the analysis). But by then CS for breech was the norm and, as the years have gone on, the number of MWs with the skills to help a breech baby birth safely have plummeted.
There are MWs with good breech skills out there - some still work for the NHS but more work independently. DD1 was born as a breech baby at home with IMs - after doing a LOT of reading, talking and thinking we came to the conclusion that breech birth wasn't intrinsically more dangerous than a CS - but that trying for a breech birth with unskilled MWs increased the risks significantly.
For more info google Mary Cronk (there's a good article here and try and get hold of a copy of "Breech Birth" by Benna Waites and/or "Breech Birth: What are my options" by Jane Evans.
You might also want to talk direct to the Head of Midwifery at your hospitals (or all the hospitals in your area) - consultants are fantastic at what they do, but they are specialists in the abnormal and tend to view breech as an abnormality best resolved with surgery. MWs are more likely to see breech as an unusual variation of normal.
re. changing hospitals - you always have a choice to do this, but it would be worth doing some investigating first to make sure doing so is going to give you a better chance of achieving your goal.
Trying to decide how to birth DD1 was one of the hardest decisions I've ever had to make. And I still question it today (she's 3 now). All any of us can do is to make the best decision for us at the time.