Building work for Trafalgar infants and junior school in Richmond, west London, was due to be completed in the summer, but pupils are still unable to use many of the facilities, including a new kitchen, because minor works remain unfinished.
The letter from pupils on Trafalgar's school council was read to MPs this week during a House of Commons debate on problems surrounding the Private Finance Initiative in education.
Trafalgar junior and infants has been among the schools affected by the near-bankruptcy of Jarvis, which has been involved in 19 PFI deals covering 120 schools.
The company accumulated debts of pound;230 million and has been given a stay of execution by banks until April to finish its projects.
The 10 and 11-year-old pupils wrote: "We are very proud of our school and are very excited about some of the rebuilding that has taken place and also some of the new equipment. However, we are at the same time extremely upset that the building seems to have come to an end before it has been properly finished.
"Take a look at our playground. It still looks like a builder's yard. The ground in some places is appalling and lots of people have fallen over and hurt themselves.
"The water fountains dribble a lot and you can't drink from them. Jarvis are making little progress and are not sticking to their promises. We are very angry with Jarvis and we will not rest until it is done."
The letter was read by Vincent Cable, Liberal Democrat Treasury spokesman and MP for Twickenham. Mr Cable said that most of the six schools involved in the pound;50m Jarvis PFI project in Richmond had been completed on time but claimed that the incident raised wider questions about the potential pitfalls of PFI in education.
David Miliband, minister for school standards, said that the pupils' words brought home this "unacceptable situation".
He said the Government hoped to learn from such mistakes as it embarked on its pound;2 billion-a-year Building Schools for the Future programme, about half of which will be carried out through PFI.
Richmond council announced on Wednesday that it was considering legal action to ensure Jarvis complied with its contract.
Jarvis has already been penalised financially for over-runs on schools projects in the North-west.
A Jarvis spokesman said the company felt "deep regret for the impact on the children" at Trafalgar. Jarvis was working closely with the school and was in discussions with another company about financing the completion of the building work.