The £2 billion tunnel, which will collect overflows from London sewers, is the biggest single sewerage project since water privatisation in 1989.
There is no planned public subsidy for the project so the cost will eventually be carried by all Thames Water sewerage customers.
Yve Buckland, National Chair of the Consumer Council for Water, said: "This is a massive project by anyone's standards and with all the associated risks and potential for costs to increase over the life of the work.
“But the big issue here is the cost, and what will eventually be added to sewerage bills is way above what customers are willing to pay.
“Not only that, the increases will mean that low-income customers will be hit particularly hard, and they will simply find their sewerage bills unaffordable.”