It's worth trying Uber, who've started hanging out locally. I live near LGW and my best price has been £38 from London Bridge home, after 11.30. I always send them to LGW after dropping me so they can get a fair back to London so it's worth looking into.

Also Roadrunners/Belfry (local taxi firm) may well get you where you want to for not far off that amount. Worth a call - although it's no limo service.

I would avoid Southern - they'll be slightly cheaper but tend to be a milk-run that time of night. The express will take about 30 mins but it could be double or more on Southern.

Good luck!