Because of the requisite tube journey, ticket buying (if applicable) and potential wait time at Paddington (could be 15 minutes if you hit it just wrong), it's a very expensive and not particularly quick or convenient way to get from StP to LHR.
I recommend you take the Underground, Piccadilly line, direct. Comparing trip times:
Whichever way you do it, first you have to allow, say, 10 minutes from alighting your train at StP to boarding an Underground train, including likely maximum wait time. Add that to:
-: via the HEX, 20 minutes by tube StP to Paddington, 5 minutes for moving within the station, up to 15 minutes awaiting departure and 15 minutes trip time. That's 55 minutes maximum.
-: via the Piccadilly Line, about 60 minutes.