Start by getting the Probate Office to carry out a search to see whether a Grant of Representation has been made (either the result of an executor seeking probate on a will or through someone applying for Letters of Administration upon intestacy). It will only cost you a fiver:
http://www.justice.go...f-probate-records.htm
However, assuming your assumption that there is no extant will to be true, then the rules state that there was no requirement to seek a Grant of Representation if the value of the estate (including property, cars, etc, as well as what was held in bank accounts) was less than £5000. However:
(i) it can sometimes still be necessary to obtain a Grant under those circumstances, in order to get access to the assets of the estate ; and
(ii) the absence of the requirement to obtain a Grant doesn't change the way that the estate must be distributed (i.e. one third each to the three children of the deceased).
If the value of the estate was over £5000, then a Grant was required before anyone could touch the assets of the estate.
Chris