A Filipino national being in Schengen area with valid tourist visa (visa C) can request a tourist visa to visit UK (standard UK visa) from a Schengen country without having to move back to his country ?
To quote from GOV.UK:
You can make applications for a visit visa or EEA family permit in any visa application centre, British diplomatic mission or consular post overseas where entry clearance applications are accepted.
You should be present legally in the country or territory you’re applying from.
Visa application centres are listed here.