This is a very difficult situation indeed.

Do you have any friends or family that would be willing to fly to DEL to pick your child up and fly back to London with them or anybody that is allowed inside the UK? (If any of my friends or family asked for such a thing I'd be at the airport in the next two hours taking the next possible flight.

(It could potentially also be a problem when you book travel for somebody who accompanies the child but that is not allowed into the UK they might deny them boarding, even if they do not plan to enter the UK. This happended to me flying to the US from Switzerland once, My passport was one of the very few special case (date wise) that would need a US visa of which I knew nothing about. Was denyed boarding when they checked the documents. Not a very nice experience.
Since the person has the UK as its final destination the argument that they don't want to enter the country might not work. I don't know enough about the UK/India flight regulations or if documents are checked before boarding in India to the UK at all, but I thought I'd just mention that this could be an issue. I'm sure somebody with more experience could clear this up).

Regarding the person who could accompany the child but not enter the UK, could you try and organize an emergency visa for them. I would definetly call the brithish consulat to check the possibility.

Another option would be to book a cheap ticket for somebody to get airside and pick the child up at the gate. But as mentioned above the hassle of having to explain this to customs etc might not be worth it.

Maybe book the arrival service of LHR? This seems to be the easiest and safest option so far.

Maybe try to call the airline and try to organize something with them. Some airlines have a very reliable UM service (sometimes even from Check-In counter to arrival hall to meet somebody to pick up the child at the destination).

Another option would be to ask somebody on here if they are arriving at the same time or earlier and would be willing to wait for the child and pick them up, I'm sure if somebody happened to arrive at the same time they would be willing, but then again I'd never 100% trust a stranger on the itnernet I've never met before. And a lot of things could go wrong there regarding delays etc...

You could ask and pay the tickets for somebody on here to fly to DEL and back to get your child and accompany them, but as mentioned above I would never entrust a stranger from the internet with my child, and I would strongly advise not to do it. But desperate situations call for desperate measures so I thought I'd still include this option.

I hope you find a good solution and that your child arrives safe in LHR.
Furthermore I wish you to get well again soon.