My immediate concern for you would be the lack of experience. You have been qualified for 18 months & have just 10 months of NHS working experience. In private practice you really are alone & need to have the clinical reasoning, skills & expertise to work confidently & independently with anything that you may encounter. Patients expectations are often higher in private practice than they are in an NHS environment. In addition, some private health insurance companies will not allow you to treat their patients with less than 5 years experience, most notably BUPA. As far as I know AXA PPP are still not recruiting physiotherapists to their register (this has been the case for several years) so you are currently unable to treat patients from the 2 largest insurance providers. This means you are limited from the outset, & as you plan to start on a domiciliary basis your target patients are those that can pay for themselves (there are further difficulties in getting health insurers to pay for domiciliary visits). In my experience self-payers make up approximately 20-30% of an established clinic patient base. So you will be competing with established local clinics who are fully equipped - you need to be offering something different / special or be particularly competitive in your pricing to attract your first patients. Working in the community is also much more time consuming so the number of patients you can see each day is considerably less than in a clinic. And you will need to advertise, advertise, advertise.
Consider perhaps renting a room on a hourly basis within a gym/sports club or complementary health centre so that you only pay for the time that you are using the room. And I would suggest that you ask your patients to give brief written feedback at the end of treatment that you can use within your advertising, & encourage recommendations by handing a few business cards to each patient.
I'm sorry if my view is rather negative as I understand & respect your desire to be working & using your skills, & the difficulties you (& so many others) have encountered in the job market in this climate. You have clearly done a lot of groundwork & if your heart tells you to go for it, then do it! I wish you the very best of luck.