You could leave the airport but you would have to take your luggage with you. I am not sure if there is a left luggage area.

The main sightseeing is about an hour's drive south of the airport so you need to bear this in mind if you decided to go ahead.

There is a left luggage depot at the International airport at Bombay which we used 2 years ago, you might be cutting it fine to take a trip into the city as the transfer from internal to the international terminal can often take up to 1 hour depending on the transfer buses.

Flying with Jetairways we checked our luggage straight throgh to LHR so took a taxi and saw the sights of Mumbai, it was fantastic. Which airline are you flying with you may be able to check your luggage through to your destination from Goa

There is no left luggage department at Mumbai airport anymore.It was withdrawn because of security issues.

John

You could hire a taxi for a couple of hours to see the sights and take you back to the airport, keeping your luggage with you (assuming the driver doesn't make off with your belongings). It's a lot cheaper than Goa. Taxi from the airport to Colaba area in the south is around 300-400 rps and there is a prepay booth near the exit.

I'm sure this has been discussed on here before, but lets assume the available 6 hrs is as stated, from landing ex-Goa to take-off to UK;
Landing (assumed to be on time) to exiting terminal with luggage, say...................0.5 hours
Check-in for International flight, usually required to be .........................................2 hours
Leaving ...................................................................................................(3.5 hours)
Taxi trip, 1 hour has been advised above, I think very tight, x2............................2.0 hours

Left for sightseeing......................................................................................1.5 hours absolute max

therefore really a waste of time and money, plus the risk of things going wrong, plus trusting your baggage on the roof of the taxi all that time (the boot is usually full of LPG cylinder)

Far better idea, this time or next, is to allow at least 24hrs between flights and stay in one of the cheapish and quaint hotels between Colaba Causeway and Gateway of India for a night or two. You will not regret it........we have done it several times.

Even better, save the cost of the exhorbitant internal flight and go back to Bombay by train for a few hundred rupees and arrive near to where you want to be. Then just get a taxi to the airport for your flight?

And don't take any of this "Its Mumbai" rubbish, remember, "We're British, we built it, it's Bombay"
............besides, everyone we know who lives there calls it Bombay automatically!

Have to agree, a few nights in Bombay is well worth it, lots to see and do and an unforgettable experience. would recommend Residency Hotel in the Fort area, nice hotel, well located close to VT Terminus and Gateway to India and very good value for money.