Thymus vulgaris (cultivated)

SW. Europe, SE. Italy (from WCSP)

Thymus vulgaris
(common thyme, German thyme,[1] garden thyme or just thyme) is a species of flowering plant in the mint family Lamiaceae, native to southern Europe from the western Mediterranean to southern Italy.
Growing to 15–30 cm (6–12 in) tall by 40 cm (16 in) wide, it is a bushy, woody-based evergreen subshrub with small, highly aromatic, grey-green leaves and clusters of purple or pink flowers in early summer.[2]
It is useful in the garden as groundcover, where it can be short-lived, but is easily propagated from cuttings.[2] It is also the main source of thyme as an ingredient in cooking and as an herbal medicine.
Numerous cultivars and hybrids have been developed for ornamental purposes. Nomenclature can be very confusing. [3] French, German and English varieties vary by leaf shape and colour and essential oils. [4] The many cultivars include 'Argenteus' (silver thyme). [5]
(from Wikipedia on 18.5.15)

Thymus vulgaris, the thyme plant, photographed from Sunnyvale, California.
Thymus serpyllum: Sending photos of Thymus serpyllum cultivated at our institutes farm.
Highly prized as spice and condiments, antiseptic, and having essential oil rich in thymol which is used as powerful antifungal agent. 

Yes .. This population seems to be different from ones I have seen in Kashmir and Manali, where the flowers have pnkish tinge.
By the way the correct name for our species is now Thymus linearis
Thymus linearis Benth., Pl. Asiat. Rar. 1: 31 1830. syn: Thymus serpyllum auct. Himal (non L.) 
Your plant with white flowers seems to be Thymus linearis var. album (B.Ghosh & U.C.Bhattach.) H.B.Naithani
Fl. Pl. India, Nepal & Bhutan 346 1990 
No sir this population was introduced from some Mediterranean country way back in 1990's at our farm by one of the researcher it is typical Thymus serpyllum L. There is lot of confusion about T. serpyllum in India most of the earlier authors reported T. linearis of Indian Himalaya with the name of preceding species. In Indian Himalaya only one species of Thyme grows i.e. T. linearis as collected by you from kashmir and manali. 
I would request you to recheck your population. Typical Thymus serpyllum var. serpyllum also has pink flowers. Your clearly has white flowers and should be Thymus serpyllum var. albus B.Ghosh & U.C.Bhattach. This according to Kew Plant List is now correctly known as  Thymus linearis var. album (B.Ghosh & U.C.Bhattach.) H.B.Naithani 
Perhaps any publication which describes or keys out the two species should help.
This link should help in understanding Thymus serpyllum
I have checked the flowers are pink in colour
I request you to compare your plant with this one and decide which one is more white
Is there any other differentiating character of T. serpyllum var. albus from the typical. Please provide me as I am not having the literature.
I have attached a photo of Thymus linearis which I have collected from Kumaon Himalaya check out the leaves they are much more linear to lanceolate while the photos I have attached has more ovate leaves. And also I have seen flowers of different shades of Thymus from purple to dark blue to pink.
You may see this links also

Key differentiating the two species (rather three T. serpyllum, T. linearis and T. vulgaris) should help. <

My linearis have prominent lateral nerves on leaves thus it is strongly going in The typical subspecies rather than subsp. hedgei which have obsolete lateral nerves.

To me appears close to images at Thymus vulgaris L. posted by ...