St. Thomas's was described as 'ancient' in 1215. It is named after Thomas Becket who died in 1170. It was probably originally part of the Monastery of St Mary Overie which was founded in 1100. So, it was probably built in the 12th Century.
St Bartholomew's Hospital was founded in 1123. If St Thomas's Hospital was originally named after Becket it may not have been built until after his death in 1170 - although it would seem strange to call the hospital 'ancient' in 1215 if it were only 30 years old. The possibility therefore exists that St Thomas's Hospital was founded in 1100 at the same time as St. Mary Overie, which would make it the oldest hospital in London (but try telling that to St. Bart's!).
St T's has roots back to the religious house of St Mary Overie founded in AD 606. Originally named in honour of St Thomas the Apostle in the 12th C, the hospital was re-founded by King Edward VI in 1553 and dedicated to the English martyr, St Thomas � Becket. The hospital was at first located in Southwark, close to site now occupied by Guy's Hospital, but moved to its current site in Westminster in 1830.