SQL Server does not allow you to use nested aggregates in the same group. One possible workaround is using the OVER() clause that I am showing below.
When you run the query below, it is probably not going to give you what you are looking for. If it does not, remove one or the other or both of the partition by clauses. (If you removed both partition by clauses, it would be just "AVG(DATEDIFF(d, ReferralRequestReceivedDate, MIN(A.AppointmentDate))) OVER () AS AvgAllocationWaitTime".)
COUNT(CASE WHEN AppointmentTypeId IN ( 1, 3 )
AND AppointmentDate BETWEEN '27 Jan 2013'
AND '13 Apr 2013'
END) AS AppsBooked ,
AVG(DATEDIFF(d, ReferralRequestReceivedDate, MIN(A.AppointmentDate))) OVER ( PARTITION BY OA.OrganisationAreaId,
OA.Name ) AS AvgAllocationWaitTime
LEFT OUTER JOIN Clients C
ON OA.OrganisationAreaId = C.OrganisationAreaId
LEFT OUTER JOIN IaptReferrals R
ON C.ClientId = R.ClientId
LEFT OUTER JOIN IaptAppointments A
ON R.IaptReferralId = A.Referral_IaptReferralId