I admire your work ethic and drive but it is going to be very hard to find a job at your age at the current time. I worked vegetable picking on a farm, collecting glasses in a pub and in a shoe shop at your age which are opportunities unlikely now.
It's a shame you feel obliged to do this because your family is poor.
Obviously we don't know your family's situation and constraints, such as disabilities, lone parent status, childcare responsibilities, outgoings like rent/mortgage.
However 2 adults over the age of 21 working full time (35 hours per week) at the National Minimum Wage can each earn at least £20820 per annum. After tax/NI, but excluding pension contributions, this comes out at £1,542.65 each, so a joint household income can be over £3,000 per month in this scenario (depending on pension contributions).
Perhaps you could look into self employment with your neighbours - babysitting, dog walking, mowing lawns/raking leaves, washing cars. Or do you live in an isolated rural area with limited public transport links?