If somone is getting the Severe Disability Premium on their IS but then their oldest child turns 18 but is still in full time education and the parent still gets Child Benefit for them can the parent still get the SDP?

Yes, as still a qualifying young person for child benefit, this counts for 18 and 19 year old's and so your client will still count as 'living alone'.

Hope this helps.

The rules for this are contained in schedule 2 of the income support (general) regulations 1987 at para 13 (2)(b)(iii).

Although the child is over 18, they will be classed as a non dependant as long as they are still in non advanced education and the claimant receives child benefit for them.