Hi Alexandra
Welcome to the forum.
You might want to have a look at the following FAQ which explains where everything is;
www.benefitsandwork.co.uk/guides-for-claimants/faq/forum The answer is ...... they are both correct
It all depends on the answer you give when you are asked, what type of ESA do you receive?
If you are only receiving Contribution Based ESA then a lump sum will not affect your ESA but a regular payment will. If the pension is more then £85/week then there will be a £1/week deduction for every £2 in excess of the £85.
If you are receiving any Income Related ESA, either in part or in whole, then it will affect your ESA. You have to have savings less than £16k to be eligible to claim IR ESA.
Gary