what weekly/yearly wage would i need to earn to take home �150.00 per week. i have been offered part time work and i need to earn that amount as minimal amount to survive and pay rent
Because you can earn roughly �100 per week before tax and national insurance kick in, you don't need to earn that much more than �150 p.w. to actually take that amount home.
If you earn �167 per week ( = �8684 p.a.), your take home pay will be �149.99. (That assumes that your employer doesn't make additional deductions from your pay, such as contributions to a pension scheme).