Birds start their reproductive cycle when they get 'hints' from the environment that tells them springtime is coming. In nature this would be warming temperatures, lengthening days, more rain and more fresh vegetables/fruits. In the livigroom we sometimes create the same signs. If winter is coming you turn on the heat. During wintertime you will have the lights on in your livingroom more often, and maybe even longer than during summertime. If you decide to go on a healthy diet, chances are you will feed the birds a lot more vegetables and fruits as well.
What is the situation? Is she alone? Does she have bird-friends? What sexe and breed are her friends? How old are they?
Just to state the obvious. Dont give her anything to lay eggs in. No nestbox, no hiding hut, no dark places to crawl into. Budgies will look at anything they can squeeze into as a nestingopportunity.
Dont take away the eggs. This will only stimulate her to lay more.
You can also try to put the cage into a room that has a lower temperature for a while.
You can try cutting down her light-hours she gets per day. Put a towel over her cage when you put the lights on.
Dont give her too many fresh food like fruits and vegetables or wet food like eggfood and sprouted seeds for a litle while, if any.
To help her get through this, give her lots of calciumrich food or suplements. She needs calcium if she lays eggs. If she doesnt get it from her food, she will deplete her own bonestructure.
Heres another topic dealing with a similar problem:
viewtopic.php?f=18&t=2073&p=10030&hilit=+not+breed#p10030