But of course, you have to have 'worked' in order to get an equity card. It's a famous catch-22.
Your best bet to start with is to find an agency that finds work for extras, or check 'The Stage' for any companies advertising for them. Once you've done a couple of bits like this (probably being paid peanuts or not at all), then you should be able to apply for an equity card and be able to go for more jobs.
I have a friend who started like this. Did a couple of walk-ons in Casualty/The Bill, and went from there. Not that she's ever so famous, but she did play the Granny in the recent KitKat ad, where she gives her grandson a KitKat wrapper in his birthday card.