Paid by mistake by work, will it affect ESA

Hiya,
I've just joined as I am looking for help and advice really.

I have been on long term sick for almost a year.
My employer refuses to change my role due to my disability, instead they are waiting for an eligibility review for income protection to take place.
As I exceeded SSP, I got accepted onto ESA.
My employer has previously overpaid me, and put me into a debt with them but I wasn't claiming ESA then.

And just this week, they have overpaid me, I am presuming by mistake as I had told them to consider me on sick until until I agree a return date.
I only received in my account just over £600 as the rest went to paying the previous over paid amounts. 
As they have paid me, and I am claiming ESA - what do I need to do if anything? How will this affect my claim?

I will be taking legal advice on my whole situation but feel this is almost the last straw with them. I have a baby, and childcare costs get a reduction because I am on ESA  and can be stopped too.

Any advice would be great thanks in advance