Thanks for your question.
From the limited information you have provided above, if you and your partner are both in the UK illegally and you have had two children since 2007, this is not a ground to obtain discretionary leave to remain.
As both you and your partner are in the UK illegally, the likely scenario would be that you would all be required to leave the UK.
If you are on a limited income, I would suggest you contact the Immigration Advisory Service (IAS) on: 0844(NNN) NNN-NNNN/strong>
I hope this answers your question. If so, kindly click accept.
If you wish to discuss, please feel free to ask further questions.
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