If your mum died without making a will, she died intestate and her estate will have to be dealt with under the rules that govern intestacy.
That means, without a surviving spouse, the whole of the estate is split equally between the blood relatives according to set rules. In your case, that will be equally between you and your brother - including the house.
So, far from your brother denying you a sum that you say was promised, he is going to find PDQ that you are actually entitled to rather more than that £16k anyway.
It may well be possible for you to vary the terms of the split such that you gift part of it back to him - of that is your wish.
In any event, you really need to see a solicitor.