Transportation options Heathrow to Gatwick

There is a regular bus service. This goes round London and is quicker than going into and out of central London. Takes 65 minutes on a good day, but could be longer depending on traffic.

• 09:25 land.
• 60-90 minutes to get out the front of the airport = 10:30-11:00
• +Wait for next bus (multiple buses per hour), +travel time to to Gatwick = 11:30 - 12:30
• Enough time to have to check in and have some food/coffee at Gatwick, provided your plane lands on time.

Details of service here: https://www.nationalexpress.com/en/airports/gatwick/heathrow-to-gatwick

Where are you headed to? If Europe you need to be at the airport at least 2 hours before you flight departs and 3 hours long haul so it could be tight.

https://www.heathrow.com/transport-and-directions/journey-planner?src=LHRA045

Any chance you can change the travel plans and use just one airport? You’re going to need everything to go right to make it. Is this on separate tickets? Is the LHR flight an overnight flight from North America? You’d have to add in jet lag to boot if it is.

If this is your USA to Milan trip and the LGW-MXP is on easyjet, be aware easyjet closes boarding 30 minutes prior to departure.

If this is the case and you have already purchased ticket, say prayers--- otherwise I would be looking for a different flight plan

If your flight arrives late at LHR, you have some significant peril for not making your LGW flight.

If my assumptions are wrong then , "never mind"

This would make me very nervous especially with the off-chance that your flight arriving at Heathrow could be running late. Can you get a flight later that afternoon?
Not sure how many bags you will have but if it is manageable I might try LHR to Paddington via Heathrow Express (15 minute ride), Paddington to Victoria station via tube (15 minutes or so - no changes), and Victoria to Gatwick via Gatwick Express (.30 minutes).
I've never taken the direct bus which is probably faster in theory BUT I have also run into nighmarish traffic on the outskirts of London that still makes me shake to this day...ground transportation there isn't always ideal.
Since you're arriving after rush hour I would consider trains and tube. That's just my personal comfort level though.