It can be concluded that perhaps both of Thomas' parents are partially Romani Gypsies, it is also implied that they have Irish Traveller ancestry too, as Polly mentions that, alongside Romani, they should not speak Shelta to Karl Thorne, which is the language spoken by Irish Travellers. It is implied by their aunt, Polly, who is their father's sister and Thomas himself when he states in Series 1 that the Lee Family are kin to the Shelby family from their mother's side.
Thomas Shelby and his siblings are Gypsies from both sides of their family.
