I suggest you get hold of The Reconstruction of Warriors by E R Mayhew. German aircrew were generally hospitalized in London and yes, burns and amputations were treated there. For example Herbert Schmidt (JG 27-badly burned) and Walter Kienzle (JG 26 leg amputated) both 30 Sep 40 casualties. Most went to the Royal Herbert Hospital
https://en.wikipedia.org/wiki/Royal_Herbert_Hospital