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I've spent hours looking into it for events this year and next.
You can do London-Barcelona in a day but not any further.
Connections to Madrid are good but to the south are not great, eg only one train per day direct Barcelona to Cartegena, one per day from Algeciras to Madrid. Those are not special examples, they're the two journeys I've looked at booking.
Coming back, the first train from Madrid to Barcelona to connect with the TGV doesn't take bikes.
Can't get to France early from beyond Madrid to catch the sleeper trains so need to stay overnight.
Also it's next to impossible to book onto Spanish trains with an interrail pass in advance. Risk is you have to hope you're lucky at the station.
It's much easier to get to / from Italy, Croatia or Poland from London than southern Spain.
Spain is quite hard by train, if it is any further than Barcelona