On ESA, etc - Can a relative give ongoing financial help?

Warning: Depressing Topic:

My elderly father thinks he will die very soon. He has discovered that, following his death, half of his pension can be paid to me, because of my disability. If I did receive ongoing regular payments, how might that affect my benefits?

I'm on ESA, Housing Benefit, and Council Tax Benefit. Would I lose all/some of these benefits, or would the amount received just be decreased? Any info hugely appreciated!

Cheers X

Hi Gordon,

Thank you very much for your reply!