Thanks for the reply.
As Fred stated, part of an estate will only go to a deceased beneficiary's children if that beneficiary was a child (or grandchild) of the testator. In the circumstances you describe, where a named beneficiary is the deceased brother or sister of the testator, his or her share of the estate does not go to his/her children. It is added to the residue of the estate, to be shared between the surviving beneficiaries in accordance with the terms of the will.
As I stated, the testator can over-ride those provisions by specifying what should happen if a person he has named as a beneficiary dies before him. For example (after the parts of the will that deal with settling bills, paying funeral expenses and authorising the executors to convert property to cash), a testator might write this:
"I leave one third of my residual estate to my brother, John Arthur Bloggs, of 23 Acacia Avenue, Sometown, in the county of Essex. Should the said John Arthur Bloggs pre-decease me or fail to survive me for a period exceeding three calendar months, this part of my residual estate shall be divided equally between those persons who are the legitimate issue of the said John Arthur Bloggs or lawfully adopted by him".
Chris