Yes it should be quite easy to travel from Gatwick airport to the venue and back, the venue is just a few minutes walk from Kentish Town underground station.
The easiest way is to get the train from Gatwick Airport to London Bridge, it departs every 15 mins in in the afternoon and takes just 31 mins to reach London Bridge, once at London Bridge station you would have to transfer to the London underground, the great thing is London Bridge is on the same underground line as Kentish town.
So its just then an easy direct 20 minute underground journey heading North on the northern line to Kentish Town, overall even with the change from overground railway onto the London underground it should only take about an hour from leaving Gatwick airport!
The last train back to London Bridge leaves Kentish town at 20 past midnight which will be well after the show ends and connects you in time to a Gatwick train, the last Gatwick train from London Bridge is at 1:05am but alternatively there are also Gatwick trains from Victoria station running every hour through the night.
Travelling in London is pretty Safe as London has so much CCTV including on all of the underground stations & trains, however late at night you may feel safer taking a taxi to either London Bridge or Victoria to get the main train back to Gatwick, which will be staffed with conductors & therefore very safe.
You can use these websites to look up the times
The main uk train timetables websites, simply start typing in Gatwick & it will auto complete to Gatwick airport and as you type in London as destination, London Bridge should be the 3rd option down
the London transport journey planner website including the underground, select London Bridge to Kentish town to check times
Hope that helps you and anyone else that may be considering flying into Gatwick Airport!