|First impressions: your Intro should be rated E, not Non-E There's nothing there that isn't safe for everyone and your piece will be listed in more places, giving you more exposure.
Spelling, punctuation and grammar are all fine; no real problems that I could see apart from the fact that you use two single quotation marks '' as opposed to double quotation marks " when your characters speak. It doesn't make it any harder to read, but it does look rather odd.
So, onto the specifics!
"Quick," she hissed ''Quick, we need to leave now!"
Hissing is a word usually associated with stealth and quiet tones of voice, like whispering. Given how loud the air raid sirens would have been, Peter might not have heard her. Why would his mother be so keen to keep her voice down? It doesn't make sense.
I liked the touch and description of the photo; that was very nicely done
One of his slipper came lose and peter was forced to continue on bare foot should be One of his slippers came loose and Peter was forced to continue on one bare foot
This also doesn't make a whole lot of sense to me. During WWII, the Royal Observer Corps kept an eye on incoming planes, often helped by coastal radar stations. The second any enemy planes were spotted, a warning would be sent to, well, pretty much everywhere but especially London. Given how fast fighters and bombers could travel, even in those days, it wouldn't take them long to reach London from the coast, but the air raid sirens would have gone off before the planes were there.
While there certainly wouldn't be time to stop and pack a suitcase (for this reason the majority of families had a pre-packed bag containing things like ID and ration books by the door at all times, so that when the siren went off they could just grab the bag and run) Peter would have had time to put on a decent pair of shoes.
An engine screamed overhead and Peter clutched his mother's hand as the plane passed overhead.
I'm not sure which part of the Blitz your story is set in (please remember that while many people make the mistake of thinking it was a one-off isolated incident, in fact it was a prolonged series of bombings that lasted from September 1940 to May 1941). There may have been searchlights enabling Peter to see the plane, so this part is fine. Try not to use the word overhead twice in the same sentence though; it might be better if you deleted the last five words (we know it's a plane; there's no reason to tell us so).
a piece of debris hit Peter in the back and his hand was torn from his mothers mother's as he was flung forward. Peter lay dazed on the cold hard ground. His mother was looking frantically for him. He could see her calling his name through tear stained eyes.
If he was flung forward, his mother would have seen him as he would have fallen in front of her. If he was flung forward, he would be lying on his stomach with his face on the ground and his mother behind him, so how could he see her? If he was thrown forward by the force of the blast, his mother would have been thrown with him.
Peter tried to rise but a stab of agony in his left leg cause him to come crashing down again.
So anyone looking at him would clearly see he was alive. Even if his mother couldn't see him (remember bombers dropped incendiaries as well as Hollywood-style KABOOM bombs, so there would have been plenty of fire to work by) and even if she decided to abandon him to save herself, which is how this reads, what about all the other Londoners who are heading for safety?
And if they all decided to leave him to die, what was the ARP doing during all this? A confirmed bombing (there were quite a few false alarms as well as the real thing) would mean they'd be out in full force doing their job, which wasn't just directing people to the nearest shelter but searching for injured people to rescue and transport. If Peter was strong enough to attempt to get up, he would definitely get their attention.
The writing itself is good, and I found myself rooting for Peter and hoping he'd make it. Your biggest problem is plausibility, both from the writing point of view (Peter falls forward in front of his mother who somehow fails to see him) and the historical one.
I wish you luck with this piece