Petition Government Funding? What is going on?

I am writing this petition with a hope to take this to parliament with a general disgust at how this country offers help to its people.
I have recently found out that an 86 year old woman who has worked for over 60 years gets NO help from our government because she is not in receipt of means tested benefits and has "savings" of which after she has paid out all of her outgoings, herself and her husband have £92 per month for food etc.
It has also been widely broadcasted that our government will generously hand out benefits to people who have been in our country for less than 6 months who have not attempted to get work, not pay a penny into our society, and learn our language or even attempt to financially support themselves? Would this happen to us if we moved to another Country?
SURELY THERE IS SOMETHING WRONG? Is there any point in us working, earning, saving and hoping to have a comfortable future when our government seems to be helping the wrong people?