Housing Benefit within the private housing sector is based upon the Local Housing Allowance. Use the calculator here to see how many bedrooms you're entitled to claim for under the rules:
https://lha-direct.vo...e/LHASearchIntro.aspx
(NB: the Calculator link won't become available for use until you've ticked where it says 'Click here .. . ").
Once you know how many bedrooms you're entitled to, use the 'Local Authority' or 'Postcode' search for find out the amount which can be paid.
If you're entitled to 3 bedrooms and the benefit shown for a 3-bedroomed property is acceptable to your brother as rent there's no reason why he can't let you rent the property. (Plenty of people in receipt of benefits have a family member as landlord).
If you're only entitled to 2 bedrooms you should check with your local council about the rules on occupying a larger house. However, as long as your brother would accept the lower rent for a 2-bedroom property, I can see no reason why you shouldn't be able to rent from him.
Chris