It is impossible to determine. Some deaths are very quickly reported to the Bona Vacantia division (often by the local Council). Others can take some time - sometimes years. It really depends on what assets there are and what is known about the deceased.
Not all cases without a Will end up at BV since very often there are relatives who will take on intestacy. It is only those without known relatives where this is likely to happen.
Generally the estate is administered and it is paid into the gov (or Duchy of Lancaster) as soon as it is administered. However, those who are entitled to claim can make a claim up to 12 years from the date it was administered. If the death was before 1997, they will admit claims for up to 30 years.