
The woman, in her 30s, and a one-year-old boy were found suffering stab injuries at a residential address in the London Borough of Hounslow on Monday evening.
The Metropolitan Police said the boy remains in a critical condition, while the woman's injures are not life threatening.
Police were still at the scene this morning as the investigation continues.
Blood could be seen on the wall and floor at the entrance to a flat in Swinfield Close in Hanworth.


At the scene they found the woman and infant suffering knife wounds and the pair were rushed hospital in west London by the Air Ambulance Service.
A witness told Sky News: 'I heard a lot of screaming and crying, it was quite distressing to hear.'
Local Tim Stollery tweeted: 'As much as I like spotting the helicopters overhead, it can't be a good thing seeing both @NPASRedhill G-POLF & @LDNairamb G-HMS in attendance over #Hanworth #Feltham #Oriel this evening.
'Fingers crossed whoever might be on board makes a good recovery.'
The Met said officers are now looking for a man who is known to live at the address and the three are believed to have been known to each other.
According to reports officers flooded the area and pictures showed police dog handlers at the scene.
No arrests have been made.
Police remained at the address on Monday night as investigators sealed off the crime scene.
Anyone with information is asked to contact Hounslow Police on 101 or tweet @MetCC quoting CAD 6981/4June or call Crimestoppers on 0800 555 111.




Comment: See also:
- Cyclist filmed in terrifying knife attack on motorist in South London
- Man stabbed to death in wealthy London borough amid knife crime 'epidemic'
- London knife crime craze: Four men stabbed over the course of five days
- London experiencing unprecedented levels of gun and knife crimes
UPDATE (June 7): Man Arrested for Double Attack Was Pakistani National Awaiting Deportation