FWIW, the Oxford Dictionary of English Place-Names records the following early spellings:
Leicester: Ligera ceaster, AD 917; Ligora ceaster, AD 942, Ledecestre, AD 1086 (Domesday Book); Legrecestra, AD 1130; Leircestre, AD 1205.
Gloucester: Gleawecestre, AD804; Glowecestre, AD 1086 (Domesday Book); Glouchaestre, AD 1205.
Worcester: Ueorgorna ceastre, AD889; Wigorna ceastre, AD 779; Wigraceastre, AD 904; Wirecestre, AD 1086 (Domesday Book).
(The ODEPN is really concerned only to demonstrate the etymology of these names, not their later pronunciation; so unfortunately it only records spellings any later than these where necessary for that purpose.)
Edited to add:
Bear in mind also that just because Leicester, Gloucester and Worcester are spelt that way it does not necessarily follow that they were ever pronounced that way. Anglo-Saxon scribes consistently spelled “London” as Lunden, showing that they pronounced it just as we do; the two O’s in the post-Conquest spelling are a product of Norman scribes and Latinity. I can quite imagine scribes who knew that the last element in those names was Latin castra insisting on giving it a value in writing that it didn’t actually have in real speech.