Thames Water has applied to the industry regulator, Ofwat, to raise bills by more than 10% above the cost of inflation over a five-year period.
The regulator said the company had submitted by far the highest proposed bill increase of any of the major water supply and sewerage firms that have put forward their plans for 2015-20.
Nine firms said they would cut bills or leave them flat in real terms over 2015-20, after Ofwat asked them to consider scaling back increases amid a squeeze on household finances.
But Thames Water said its plans to invest £2.8 billion in the Thames Tideway Tunnel, a major new sewer, mean it must add £8 above inflation for each of the five years from 2015 - and that without this, bill rises would be below inflation.
Ofwat figures show the supplier plans a 6.8% real terms cut in average water supply bills but a 34.8% increase for sewerage, giving an average real terms rise of 10.4%.
Thames Water serves 14 million customers in and around London. The current £358 bill would increase to £398, plus inflation, by 2020.
Chief executive Martin Baggs claimed seven out of 10 customers found the plan "acceptable", with the capital's Victorian water and sewerage infrastructure in urgent need of upgrading.
– Chief executive Martin Baggs
"It is clear that bill increases are only acceptable if they are absolutely essential, but customers have told us to avoid storing up problems for the future."Our plan will deliver value for money on the things our customers have told us matter most."