It's quite likely edam - you'd need to contact City of Westminster Archives I think.
see here for specific boro'/ward details
I also found this from a history of St Thomas' hosptial website
"St Thomas's Hospital and Medical School were seriously disrupted by the second world war. The hospital's status as a casualty clearance station, with sixteen wards closed and a limited out-patients' service meant that clinical teaching was impossible. Students were dispersed among other London hospitals and the pre-clinical school went to Wadham College, Cambridge. By March 1940 the anticipated aerial bombing had not taken place, and the medical school had reformed, the out-patients' service resumed and 250 civilian beds opened at Lambeth. However bombing raids in the Autumn severely damaged the hospital. Arrangements were made to move staff and patients to a hutted hospital at Hydestile, near Godalming, which had previously been occupied by Australian troops. By 1943 St Thomas's Hospital comprised 184 beds at the London site, 334 in Hydesville and 50 maternity beds in Woking. By the end of the war four ward buildings, three operating theatres, most accommodation for nurses and a large section of the out-patients department had been destroyed."
and this from the BBC WW2 memories website
"Later that year, in October l944, I started training as a physio at St. Thomas?s Hospital in London. Initially we were evacuated to Hydestile Hospital, near Godalming in Surrey, and billeted in nearby Milford. We were required to learn basic first aid so that in a real emergency we could be asked to work as nurses on the wards. Interestingly, the patients were exclusively from London and one of my memories is of hearing from Eastenders whose only previous time in the country was ?opping in Kent each summer. We cycled everywhere from Milford and I remember one day in the bitterly cold winter of ?44/45 cycling to the cinema in Godalming. There was no question in those days of wearing trousers, and we had bare legs instead of stockings as it was easier to chip the ice off bare legs!
After six months, we went back to London for the next part of our training, and fortunately this commenced the day after the last doodlebug fell on London. A very badly damaged ward at St. Thomas?s was made available to student physios as a classroom and much of the department was in the basement. We did some of our training at St. Peter?s, Chertsey, then an orthopaedic unit. We also visited a maternity unit, which was at Ashdown House in Woking."