Just temporarily change the session-level date format like this...
--===== This simulates the issue the OP described.
PRINT 'Using MDY...';
SET DATEFORMAT MDY --Session level setting here.
;
SELECT CONVERT(DATETIME,'19/08/20 07:23:42'); --This fails.
;
GO
PRINT REPLICATE('-',119);
GO
--===== This is the simple fix within a proc
PRINT 'Using DMY for the session level setting...';
PRINT 'Doe NOT change the server level setting!'
;
SET DATEFORMAT DMY --Session level setting here.
;
SELECT CONVERT(DATETIME,'19/08/20 07:23:42'); --Now it works.
;
GO
See the following link for more information.
REF: https://learn.microsoft.com/en-us/sql/t-sql/statements/set-statements-transact-sql