A carcass ply is applied around an outer surface of a building drum according to an application diameter larger than the fitting diameter of a tyre. Coaxially engaged around each of the end flaps is an annular anchoring structure defining the fitting diameter. A pair of sidewalls is manufactured by laying of a continuous elongated element in the form of approached coils on the carcass sleeve. An outer sleeve, including at least one belt structure possibly associated with a tread band, is coaxially centered around the carcass sleeve. Through axial approaching of two halves forming the building drum, the carcass sleeve is shaped into a toroidal configuration to determine application of same against a radially internal surface of the outer sleeve.