I started my career by being the office dogs body at White Waltham back in 1971. Wound up retiring as a 767 Captain four years ago, so it can be done.
Nothing beats initiative and enterprise so get around all the airfields you can commute to, or are prepared to live near and poke your head around the door of clubs and FBO's. Asking face to face is the best way to get in.
Good Luck.