2 years ago I was in the exact same position as you. We were only going to move for the exact right house and they don't come up much in the area we live in.
It took almost 18 months but we did it. We had our house ready to sell, when the house we wanted came up we quickly got our house on the market, and made sure our estate agent made viewers aware of our position etc.
Our vendors were in the exact same position too. At one point the house they were buying fell through so the chain waited about 6 months while they found a new house.
(Our buyers were a couple who were going to keep their flat and renovate our house so they were happy to wait).
But, it is very much the luck of the chain. It relies on the right people being in the right position at the right time.
We didn't view until our house was under offer. There wouldn't have been any point anyway because at each point the chain below needs to be proceed-able.
E.g.When our vendors saw a house they loved, the people selling it wouldn't accepted their offer until they knew our vendors and us were under offer and our buyers had demonstrated proof of funds.
This might be the same for the owners of the house you like; they might have seen a house they want to buy and they need to be as desirable a buyer as possible when putting their offer in. Having an incomplete chain below them is not desirable.
For those saying it's crazy or doesn't make sense to not be able to view until you've sold; it's literally how the housing market in England operates and is how the vast majority of house sales happen here. So it might not make sense to you but it is the way it's done and clearly it works.
It is also shit; it's why moving is so stressful and why so many house sales fall through. But that's life sometimes.