April Jones' parents, brother and sister followed the horse-drawn hearse on the one mile journey from the Bryn-y-Gog estate to St Peter's Church in a car.
They were joined by hundreds of mourners on foot, with many wearing the schoolgirl's favourite colour pink.
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The country's counter-terrorism forces have regained control of the facility.
The commissioner of the Metropolitan Police has said he cannot promise the public an attack will not take place.
The showers are likely to be particularly heavy across northern parts of the country.