It is not defined anywhere.
Actually, it is. JAR-FCL 1.005, at Amendment 7, defines cross country as
"A flight between a point of departure and a point of arrival following a pre –planned route using standard navigation procedures." Now, before everyone starts bleating that Amendment 7 is not implemented in the UK, it will have to be at some point prior to the adoption of the EASA Implementing Rules (i.e. before April 2012). It would therefore seem wise, in the case of a relatively long-term venture such as the OP is suggesting, to ensure that ones cross-country flying meets the Amendment 7 definition.
Solo for this purpose means the only licensed pilot on board, you can have non flying passengers in the aircraft.
Solo means solo and JAR-FCL 1.005 defines solo flight time as
"Flight time during which a student pilot is the sole occupant of an aircraft." However, JAR-FCL 1.155(c)(2) does not require 20 hours solo cross country flight but
"20 hours VFR cross-country flight time as pilot-in-command" so you can have anyone you like in the aircraft with you so long as you are the nominated PIC.