On the morning after Tim Yeo's resignation from the Government none of the broadsheet newspapers described his illegitimate daughter in these terms, with the single exception of the Independent, whose reporter put 'love child' in inverted commas. I am not sure who he was supposed to be quoting; perhaps he was using the marks merely to distance himself from such a quaint expression, as being not his, or the Independent's, sort or thing.
The tabloids, on the other hand, could hardly keep away from it, using it as though it were an everyday word ('The love child issue' - Daily Express). It is just a bit of a puzzle, until one remembers that the popular papers, for all their claim to be speaking the language of the people, have a vocabulary of their own. It includes other love combinations never found outside their pages: love tangle, for example, when divorce (generally bitter) is in the air ('Love tangle Sally bids for 'Fix It' slot' says the Express on the page after its piece on Mr Yeo's love child). When custody is disputed, it's a tug of love. And Mr Yeo himself is a love cheat (Mirror) though he is also a sex cheat (Daily Star) which I think a mistaken use, for popspeak, though often confusing sex and love, has rules about which word should be applied. (Romps are always sex romps, never love romps.)
The expression love child was always odd, though, with its implication that a child born out of wedlock was necessarily the product of a loving union, while one legitimately conceived was not. The broadsheets are wise to avoid it.