Still poking my nose in.

As far as I understand it, your partner needs a visa to leave PH and enter UK
To be honest I'm not sure what happens about CFO clearance requirements these days.

Just to say that LGBT is not well understood or catered for here in the Philippines.
I'm not sure just which way either Immigration or CFO might jump.
There's also an age angle too to consider

OK, I can only share what some friends experienced and shared with me. Maybe I don't know all their 'insider info' but here's what they told me in 2015.
They told me they went to CFO and CFO said yes they need a sticker and the Filipino 'fiance'
needs to attend the Seminar.
The Filipino same sex partner attended the seminar, got approval and received the sticker.

To be honest I just don't know where either CFO or immigration stand on this these days but better be safe than sorry IMHO and check, check and check again.
One thing is for sure, the Immigration Officer at Philippines departure point can refuse boarding.
May I suggest you double-check that one with the CFO