A flow chart might help:
http://www.justice.go...ate/probate-guide.pdf
If you find, from the information that Tamborine and I have posted, that you appear to be 'top of the tree' when it comes to inheriting from the estate (either solely, or jointly with others), you should apply to the Probate Registry for a 'grant of representation' to allow you to distribute the estate in accordance with the intestacy rules. (Since the cousin died intestate, the grant will be in the form of 'letters of administration').
Unless the estate is particularly complicated (or there are difficulties in determining who has the right to inherit), you do NOT need to use the services of a solicitor. (Probate registry staff are, in my experience, wonderfully helpful).
Probate registries are listed here:
http://www.justice.go...robate-registries.htm
To get the contact details, click 'Court finder', set 'Search by court type' to 'Probate', leave everything else blank and click 'Submit'.
Chris