The UK CAA define x-country time as:
More prosaically, it is how the European Commission defines it.
Looking at the requirements for obtaining, say, a LAPL(A), Part-FCL describes the solo requirements as follows:
FCL.110.A LAPL(A) — Experience requirements and crediting
(a) Applicants for an LAPL(A) shall have completed at least 30 hours of flight instruction on aeroplanes or TMGs, including at least:
(1) [...]
(2) 6 hours of supervised solo flight time, including at least 3 hours of solo cross-country flight time with at least 1 cross-country flight of at least 150 km (80 NM), during which 1 full stop landing at an aerodrome different from the aerodrome of departure shall be made.
(b) [...]
As sub-para (2) only specifies one cross country flight to land an aerodrome different to that of departure, it is my opinion that unless otherwise stated, cross-country flights can start and end at the same aerodrome.