The figure is more than London Underground (LUL) said it wanted Tube Lines to spend, but less than Tube Lines lobbied for.
Tube Lines estimated spending £7.2bn, while LUL projected £4.1bn. However, the LUL estimates excluded differential inflation which Tube Lines set at £1.2bn and which the Arbiter considers will be around £500,000 over the course of the next Review Period.
PPP arbiter Chris Bolt said: "My assessment is that costs are likely to be in the range £5.1 – 5.5 billion for the second 7½ years of the contract. I have reached this view on the basis of a detailed review of the figures put forward by Tube Lines and London Underground, and other evidence including benchmarking with other metros.
"One of the objectives of this reference was to make it more likely that the Periodic Review would be successfully concluded by 30 June 2010. It is vital, therefore, that lessons are learned from the work that has been undertaken.
"I intend to continue work with Tube Lines and London Underground over the next few months to try to reduce uncertainties further, and to clarify the procedures for the remainder of the Periodic Review," he said.
LUL managing director, Tim O'Toole said: "We do not have the option of scaling back the works to offset this expected demand because the Tube will become less reliable and its capacity will shrink at a time of growing demand, and, in any event, the PPP contract produces an increase in operating charges as a result of any reduction in capital spending, thereby frustrating attempts to cut funding demands.
"The difference in the costs budgeted for by TfL and those produced by the Arbiter are in large part in the inscrutable areas of so-called 'central costs', differential inflation and risk.
"The premiums to be paid in these areas are a result of the PPP structure," he said.