When I was a training captain on VC10s back in 1976, new captains were required to practise a double engine failure on take-off followed by a two engine approach, go-around and landing. We never closed the HP cock in my day. The procedure, if I remember correctly, was to close one throttle just after V1, followed by the other on the same side at around 100ft. I always thought the first part to be a bit hairy and so was very cautious. As the trainer in the RHS, I would close No. 4 first, followed by No. 3 and I always kept my hand on that throttle until I knew the trainee had it all under control and climbing safely away.
We always did it at a light weight and, by keeping my hand on the No. 3 throttle, I could always add a little power if the initial climb performance looked a bit too marginal. Thereafter, round the circuit and for the approach, go-around and landing, it was all straightforward. It was never done as a 'surprise test'; always as a confidence building demonstration.
There were two genuine double engine failure incidents during route flying. This one at Heathrow
Incidents and Accidents
Also, another in the US, I think out of New York, followed by a safe landing. Perhaps Jelle Hieminger has the details. I seem to recall that the captain elected to keep one of the engines running for a while, even though it had a fire warning, until he had everything sorted out. After the event, he was criticised for this (most unfairly) even though it proved to be absolutely the correct decision.