Frank Whittle was the first to register a patent for the turbojet engine in 1930.
Frank Whittle demonstrates a working prototype jet engine in 12th April, 1937.
The first plane to use a Whittle engine (Gloster E28/39) flew in 15th May, 1941.
So, Ohain's engine took the sky before Whittle's, but the Whittle engine had already been designed, tested, and confirmed before then. It's impossible to believe that Ohain never heard of, or saw, Whittle's engine before completing his own.
I think it's fair to say that Whittle invented the jet engine.