Rehan Khan, 25, is accused of attempted murder after the baby boy was left in a critical condition in the attack in Feltham on Monday. The woman’s injuries were not life threatening.
Members of the public have been advised not to approach Khan – who has links with areas including Hounslow, Isleworth, Newham, Slough and Hammersmith and Fulham – but instead to call 999 if he is seen.
Police are trying to work out whether he was staying at the house in Swinfield Close where the attack took place. They say he is known to the victims.
Officers and paramedics, including the air ambulance, were called to the home just after 7.10pm on Monday.
A neighbour 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.”
According to reports, officers flooded the area and pictures showed police dog handlers at the scene.
A large blood smear could be seen on the white wall at the entrance to the terrace house, which was cordoned off, and a police tent had been erected in the back yard.
Myrtle Cantwell, 62, who has lived on the estate for 38 years, said: “The air ambulance was hovering and there was lots of police.
“The police came by and banged on the door where it happened. The lady next door came out and ushered them in.
“I could see the police vans and the sirens but I stayed indoors.”
She said she did not know the family involved, but had
She added: “It is not a nice thing to happen is it? You do not expect that sort of thing to happen on your doorstep.”
A neighbour, 29, who would only give his name as S, said he did not know the family involved but had seen children around.
He said: “We heard the police break in through the fence and saw a bunch of officers turn up.”
Leanne Gidlow, 33, who lives on the estate, said: “They were quiet and just kept themselves to themselves. I don’t think they had been living there too long.”
She said it had just been a normal evening when suddenly she could see police.
She said: “The next thing there was armed police and they were taking everything up.
“I just think how could anyone do this? When this sort of stuff happens on your doorstep – I just turned cold.
“Then you hear there is a baby involved and it seems to make it all worse somehow.”
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.