Programming? See previous answer. I would suggest maybe writing to a magazine with game reviews if being a writer interests you rather than programming.
I know for a fact there is a SEGA Headquarters if you go Westbound from the Chiswick roundabout on the M4 you can see it on your nearside!
I cant say for sure if this particular building is still operating, but it may be good for you as a jumping off point to see how you could get into the industry.