Our litter of whippets is a week old.
The runt of the litter I thought was thriving, he is putting on weight and suckling well.
However I have noticed today her spine is very bent.
After loosing one of the pups to an accident during the labour with the mother accidentally biting the pup opening the sack, I am scared for this pup. I wouldn't want the pup to be put down. He's a dear little chap and I thought was doing so well.
Will the vet now insist he is put to sleep? I'm distraught

Others will give you more specific advise but a vet cant insist. 
They  can and will give you advise for you to consider and you can always ask for a second opinion from a specialist if you wish.
Hopefully it wont be as bad as you fear

The vet can’t insist anything, but you need to discuss how this will affect the rest of his life and if you’re happy to keep him if he can’t be sold.
Was it bent at birth or do you think that it’s happening  as he’s growing ?

Depending on the severity of the bend you could be sentencing him to a life of pain if you kept him alive, I know with humans spine deformities tend to be very painful.

He was born tiny so small all ribs were visible.
I didn't notice the bend then but he has hardly any muscle. I've only noticed it now he is growing muscle. The bend is quite severe. It is such a shame as he is doing so well. Keeping home wouldn't be a problem as we have a huge field perfect for whippets but I wouldn't want to make him suffer. This litter has been tragic and I don't know why.
We had one still born with a severe umbilical hernia, one who came out feet first got stuck and she injured it so badly I had to take it to the vets to be put to sleep and now this.
All I can think is that we kept stealing nappies put of the bin and maybe it was the chemical

No vet can insist on putting him to sleep, but if his future is going to be painful and he'll be unable to live a normal life, it would probably be the kindest thing to do for him, poor little soul.

I agree with chaumsong and Jeangenie.

see what the vet says. if the vet thinks he is not in pain and can carry on then realise this one you will be keeping as his future will be uncertain long turn and it would be cruel to let a pet owner have him if there is any doubt in his long turn prospects.  terribly sad- just give him a good life now and go with vet advice.

Bent how .... overly roached, even for a Whippet?   You should have your vet check him and take his advice but again, no vet can insist he's pts.  

I have two puppies, different litters where I had, on my vet's advice re their futures, to let them go.  The first was a puppy born with a malformed front paw (toes) and since the majority of the weight in my breed is born on the front legs, we all felt he'd have problems later on.  The other from an earlier litter, had a very delayed birth and it became very obvious that she'd experienced oxygen starvation and was affected.  She had NO control over pee or poohing.  We kept her to 18 weeks, to give her a chance, but eventually, again with the advice of our vet, made the very sad decision to let her go.   I couldn't have let her go to anybody and risk them getting angry with her re her problems and she'd have been equally difficult within our small 'pack'.   On neither occasion did my vet insist I had them pts. even if I took his advice.

That's so sad Mamabas, I had to make a similar decision with a pup from my first litter, she had developed a vascular ring anomaly, which meant that she struggled to keep liquid/food down.  There wasn't really much sign of it at first, but as she grew and was weaned it became more and more of a problem.  The vets gave her a barium meal and x-rayed, and sadly they said that even if they operated there was no guarantee the operation would work, so I made the decision to have her put to sleep there and then without reviving her.  Her prospective owner was devastated as well, I'd kept her on as I felt there was possibly a problem and until it was sorted out I wasn't going to let anyone take her.

> I have two puppies, different litters

Sorry, that should have been I HAD two puppies, different litters.......