Around 1,000 EDL protesters have made their way along Whitehall before taking a position on the pavement across the road from Downing Street.
A much smaller group of anti-fascist demonstrators gathered opposite them holding an "EDL Racists" banner.
Both sides traded insults but were kept apart by officers and barriers.The EDL supporters chanted: "We hate Cameron."
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Charlie Gard will "inevitably" die shortly after being moved to a hospice and having life-support treatment withdrawn.
The service has 1,366 people rammed into a dozen carriages designed for just 640.
The deadline for Charlie Gard's parents to reach an agreement with doctors on arrangements for his death has passed.