flight to Venice

We have done that Heathrow to Gatwick transfer on British to get to Venice. It does work, using the dedicated bus from airport to airport. After a long flight from the west coast it is not my favorite thing, so subsequently we have built in an overnight or two in London. What time does you flight get in to London?

BA flies nonstop to Venice out of Gatwick.

Unfortunately BA has only one flight daily from Heathrow to VCE. There are however more flights from LHR to Bologna BLQ (3 departures daily) or to Milano Linate (LIN). But then you would need to take the train from there (~ 1.5 hrs from Bologna, a little longer from Milan). it might be an opportunity for seeing either one city for an afternoon. The other alternative is to make a stop in London for a couple of days (it's worth it, although London isn't cheap) and then go to VCE from LGW.

I arrive in London at 6:00 AM and have 3 hrs to catch the flight to Venice.
How does it work with the luggage?

Like Roberto says, you could go from LHR to Bologna on British Airways and take the 1 hr. train into Venice. Aerobus-BLQ is the express shuttle linking Marconi(Bologna) Airport to the Bologna Main Railway Station. The bus ride to Gatwick would be about a 1 hour ride if traffic's okay. They're doing some road construction between the airports, however. Gatwick's just not the model of efficiency, so 3 hours on the ground may not work for you.
Your best and simplest bet would be fly into Bologna.

There is a 9:15 am flight from Heathrow to Venice on BA. What is wrong with that one? Your 6:00 am arrival gives you 3 hours 15 minutes to catch that flight.

You are right and 3 hrs is enough To make the BA flight out of Heathrow
Thanks for the advise