Speaking to our reporter, Liz Wickham, the travellers say they're Irish and have nowhere else to go.
The six caravans are parked on football pitches, preventing some of the regular Saturday morning matches from being played.
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Police armed with assault rifles, wearing stab vests and headgear have been seen at the house in Smallfield since 6am this morning.
A total of 35% commuters on services into Blackfriars stand, with almost a third at trains into other stations.
Joe Campbell said he wanted to adopt Kiran Sheikh but was told he couldn't because he wasn't married.