As redcrs say, you need to look into this more.
As a stay at home mum, living with her partner, you will nto be entitled to any benefits such as income support, JSA, etc. You will be entitled to working family tax credits and of cours child benefit. Family tax credit depends on what your partner earns, ie:
�o earned with one child under one = �2935 per year
�5000 " " " " = �6370 " "
�10000 = �5305
�15000 =�3455
�20000 =�1605
�25-50000 =�1090
(taken from HM Revenue & customns doc T9P 70-21
Hypothetically, if you were a single parent and living on you own and supporting your child alone you would probably be better off. This scenario would of course pose difficulties for you, as presumeably it would not be true and would leave you open to charges of fraud should you be found out.