well 'all you need' is

evidence that your relationship is genuine.
that you can support them without recourse to public funds - having a job and 6 months of pay slips, 6 months of bank statements showing you have some savings (£2,000+)
a place for them to live without it be 'overcrowded'
and because your g/f has children evidence of 'sole responsibility' and she has custody
does the children still have contact with the father ? is he named on their brith certs ? has your g/f always looked after them?