Liam - who has 12-year-old son Gene with Nicole - is believed to have moved around the corner in the posh Hampstead district of the UK capital.
A source close to Nicole - who has been with Liam since 2000 - told The Sun newspaper: ''She's spitting feathers, he's behaving like a brat.''
Liam, 40, split from Nicole in July after it emerged he had fathered a lovechild with American Journalist Liza Ghorbani, 39. He has since started divorce proceedings, hiring Sir Paul McCartney's former divorce lawyer, Fiona Shackleton.
He is now thought to be romancing his former assistant Debbie Gwyther, and planning to tell his family how he feels about her.
A source has previously said: ''They are 100 per cent together and completely in love. As it stands they are living in limbo, hiding away, unable to properly go public with how they feel.
''But once divorce proceedings begin Debbie will feel more reassured that Liam is genuinely serious about her and they can start planning for their future together.
''With that in mind he is going to sit down with his family in the next few days and tell them just how much he cares about Debbie.''
Liam also has son Lennon, 14, with ex-wife Patsy Kensit, and daughter Molly, 15, with Lisa Moorish.