I don't see any problem if you can prove that there is no father around and that you and your partner are her main source of support.

I have brought two children here in similar circumstances.

Carry out as much research as you can as to current immigration regulations/documentary requirements (UKBA website) before filling in forms and paying out money. Also requirements at the Phils end.

Her mother will have to accompany her to the UK, as the Phils authorities will not permit an unaccompanied minor to travel...especially a female.

Probably best to get her her own passport. (I know we did that with my stepkids, who at the time were aged 7 and 9 years).

Wishing you the best of luck, and stick around here because others will have advice too, and more up to date than mine.