Bob
The information about Minnie Johnson was taken from a copy of the Register of the General Nursing Council for England and Wales. Although they're not easily available, I happen to have one here for 1928 when her permanent home address was 'Stella Maris, Hall Lane, Walton-on-Naze, Essex.' The only other copy I have is for 1942, in which she doesn't have an entry, so either married or not working as a nurse by that time.
The London Hospital is probably one of the most interesting to research as they have one of the best archives in the country. I see you don't live in the UK, but here we have had a fairly long running TV series called (variously) 'Casualty 1901', 'Casualty 1907', and the latest 'Casualty 1909.' This series could I suppose be called 'faction' and follows the life of the hospital over the first decade of the twentieth century. Because it's based on the extensive hospital archives, it is, for a drama-documentary, extremely faithful to history, despite the nurses all being unusually beautiful, devoted, and with the highest integrity! The matron at the time Minnie started there was Eva Luckes, one of the most well-known and charismatic of all hospital matrons. She died in February 1919, still holding her position, and it must have been a momentous time for the hospital. A web search for her will lead on to more about the hospital at that time.
The London Hospital did a lot of things differently from others. It had a committment to the working people, and would not admit any patients who could afford to pay to go elsewhere, although they did send their nurses out after two years training to care for the rich in their own homes - that's how they made quite a lot of money to run the hospital. Many other hospitals opposed the way The London was run, and during the twenties and thirties it had no option but to fall in to line over the way it trained its nurses.
Unfortunately I'm a real one-trick pony, and as far as Elizabeth Trow goes, I'm not sure how you find her. Ancestry has British medical directories online from 1859, but I can't see an entry for her in the years following on from 1871 in that name, so perhaps she never qualified as a doctor. I guess that usual family history methods of census/BMD etc., might find her later. Maybe the occupation board here might have more ideas.
Regards --- Sue