Sorry for the delay folks. I waited for something from Waluka, before I give my opinion on Migara’s contribution on the history of Sinhala people.
First of all I haven’t done any research on the anthropology of Sinhala people when I suggested that we have many traits common with Dravidian masses. I accept that Sinhala language is linked to Pali / Sanskrit which are Indo-Aryan Languages of the past. These Indo Aryan languages derive from Proto – Vedic language that the Original Aryans used. So we have no conflict in this regard.
My view was based on LOOKS. We look much more like the Dravidians of South India than Aryans of neither India nor Europe. We specially look much more like inhabitants of Kerala. I have run into many Karalee’s thinking that they are Sinhalese at many malls in Mead East and Europe during my overseas stays. I travel alone at times and have to spend upto a week in some god forsaken city. So I do hang out in malls, to kill time and think that I will run into one of my own kind, to share a beer and a little chat. I can spot a Tamil, a mile away, but these Karalee’s make me dizzy. Many a time I have approached them thinking they are Sinhalese. So I made the conclusion that we share some ancient relationship.
But after these convergent views supplied by Waluka and Migara I checked up the Wikipedia on Sinhala People. The following is what I found there. I have left out some things to make this post a little shorter.
The Sinhalese are the main ethnic group of Sri Lanka. They speak Sinhala, an Indo-Aryan language and number approximately 15 million people with the vast majority found in Sri Lanka, while more than 300,000 live in other countries, mainly in Southeast Asia and the Middle East
Legendary accounts relating to the Indian epic saga, the Sanskritic Ramayana, discuss largely unverifiable events of deities battling over the fate of the ancient island of Lanka (presumably modern Sri Lanka), as the name of the island and its various peoples are often traced to the peoples and places named in the saga or some analogues that are believed to represent them. The Sinhalese derive their language from Indo-Aryan invaders from India who are believed to have invaded the island of Sri Lanka sometime around 500 BCE.
According to local legend, the Sinhalese are descended from the exiled Prince Vijaya and his party of several hundred who arrived on the island between 543 to 483 BCE after having been made to leave their native regions of Orissa, Bengal and elsewhere in India. The recorded history of the Buddhist Sinhalese can be found in two large chronicles, the Mahavamsa, written in Pāli roughly around the 4th century BCE, and the much later Chulavamsa (believed to have been penned in the 13 century CE by a Buddhist monk named Dhammakitti), which are considered unique in terms of age and longevity, and cover the histories of the powerful ancient kingdoms of Anuradhapura and Polonnaruwa. The name Sinhalese comes from the Indo-Aryan term Sinhala, meaning the lion people. Buddhism was an early element introduced to the island by Ashoka's son Mahinda during the 3rd century BCE and so the Sinhalese identity, combining their Indo-Aryan language and Buddhist faith, has defined much of Sri Lanka's history ever since.
Sri Lanka was home to aboriginal populations including the Veddahs and later Dravidian peoples who largely merged with an invading Indo-Aryan population of indeterminate size. Race as such in Sri Lanka has little basis in either anthropology or genetics, although variations do exist between some Sinhalese upper class group such as the Kandyan in contrast with the tiny remnants of full-blooded Veddahs, but intermingling has long blurred any substantial and general variations in the population. In fact, some early genetic tests (Y-chromosome and MtDNA only) show that the majority of the Sinhalese genetically cluster with both the Tamils and other Indic populations.
Genetic and anthropological assessments
Contrary to popular opinion, in part instilled by British colonial policy of 'divide and rule, the Sinhalese are not a distinct group that is entirely or even mainly of 'Indo-Aryan' origin, which is itself a linguistic categorization and not a palpable 'racial' group. In fact, most Sinhalese, like most Indian populations show a high degree of genetic similarity that stems from a population that formed on the island roughly 12,000 years ago and has been little changed through invasions by Indo-Aryans and other groups. A 2003 Stanford study analyzing the origins of various South Asian populations (including 40 Sinhalese and over 90 Tamils from Sri Lanka) found that most of the population of the island and India in general:
Taken together, these results show that Indian tribal and caste populations derive largely from the same genetic heritage of Pleistocene southern and western Asians and have received limited gene flow from external regions since the Holocene. 
These findings are corroborated by numerous other studies including a 2004 Biomedical Central Study:
Gene flow from West Eurasia-Broadly, the average proportion of mtDNAs from West Eurasia among Indian caste populations is 17% (Table 2). In the western States of India and in Pakistan their share is greater, reaching over 30% in Kashmir and Gujarat, nearly 40% in Indian Punjab, and peaking, expectedly, at approximately 50% in Pakistan (Table 11, see Additional file 6, Figure 11, panel A). These frequencies demonstrate a general decline (SAA p < 0.05 Figure 4) towards the south (23%, 11% and 15% in Maharashtra, Kerala and Sri Lanka, respectively) and even more so towards the east of India (13% in Uttar Pradesh and around 7% in West Bengal and Bangladesh). The low (<3%) frequency of the western Eurasian mtDNAs in Rajasthan may be in part a statistical artifact due to the limited sample size of 35 Rajputs. 
Overall, the evidence supports the strong possibility that the Sinhalese are largely indigenous to Sri Lanka and adopted the Indo-Aryan language from invaders who in turn showed limited ancestry from some original Indo-Aryan invaders stemming from some Eurasian homeland. Ultimately, the genetic evidence also shows substantial genetic drift that corresponds to geography and in the case of Sri Lanka supports the notion that most Sinhalese stem from very early migrants, rather than later invaders:
Modern Pakistani, Indian, and Sinhalese donors, examined for combinations of mini- and microsatellite loci, along with a number of Y chromosome and mtDNA markers (24), show varying degrees of diversity, which is expected from their geographic position and ability to receive waves of migrants pulsing from Africa and West Asia at different times. DYS287 or Y chromosome Alu insertion polymorphism also clearly demonstrate the gradual decline in insert-positive Y chromosomes from Africa to East Asia, reaching a transition point from polymorphic levels (1 to 5%) to private polymorphism in Pakistan. 
Thus, not surprisingly other studies done from different perspectives and goals substantiate these findings. In a 2003 American Journal of Human Genetics study entitled The Genetic Heritage of the Earliest Settlers Persists Both in Indian Tribal and Caste Populations, the 'West Asian', presumably Indo-Aryan and other, genetic indicators show that,
Their frequency is the highest in Punjab, ∼20%, and diminishes threefold, to an average of 7%, in the rest of the caste groups in India... 
These findings all include sample groups from Sinhalese populations in Sri Lanka who were thus compared to other South Asian and other Eurasian groups. From an anthropological perspective, the modern Sinhalese represent a fusion of a wide variety that nonetheless is overwhelmingly indigenous to the island of Sri Lanka and the genetic variations (based on Y-chromosomes and MtDNA only) between the Sinhalese and their Tamil and Veddah neighbors appears to be largely marginal and may be restricted to a small degree of sporadic differences rather than anything universal although some genetic drift has taken place that corresponds to language barriers.
I have only cut and pasted. Every one is welcome to log into Wikipedia to learn more.