The latest estimate of the cost of HS2 and a timetable to complete construction of the high-speed railway will be set out by the government on Tuesday, including plans to run trains slower to trim costs.

The transport secretary, Heidi Alexander, is expected to give the first official reckoning of the troubled project’s budget in 2026 prices, which HS2’s backers hope will remain substantially below £100bn.

She will also set out when trains are expected to start running between London and Birmingham as part of the long-awaited “reset” of HS2’s construction and contracts. Last year the project was delayed beyond 2033.

The HS2 Ltd chief executive, Mark Wild, is understood to have given the full findings of his review of the project several months ago, and ministers have been considering whether further cost savings were feasible or desirable, including reducing the top speed of trains from 360km/h to 320km/h, nearer the standard European limit.

Plans to build the line with automatic train operation may also be jettisoned. The system does not replace drivers entirely but is primarily used on the busiest metropolitan rail lines with high-frequency services to manage train movement for maximum capacity.

The changes appear likely after excerpts of a further critical report listing HS2’s “original sins” were briefed out by the Department for Transport, including criticism of the “gold plating” of the initial project design and “focusing on the highest possible speeds”.

The report, commissioned by Keir Starmer and written by the former national security adviser Stephen Lovegrove, echoed a review conducted by James Stewart last year into the costs of HS2 and major infrastructure projects.

Lovegrove’s report said interviews with senior officials involved in HS2 showed the damage done by “changing objectives and political priorities”, as well as awarding some of the biggest civil engineering contracts too soon without sharing the risk of escalating prices.

He found that there was “little doubt that all players, certainly at HS2 Ltd and the Department [for Transport], felt under significant pressure from ministers to keep things moving”.

It added: “As one interviewee put it, the questions are therefore ‘why [the government] failed to identify and act on the scale of failure in the company’ and whether ‘it was reasonable to assume that the department had reasonable oversight’?”

A government source said: “The Lovegrove report further confirms the astonishing extent to which previous Conservative governments had totally lost control of HS2, frittering billions of taxpayer’s money away and leaving the project no closer to being finished than when it started.

“It has been a sorry mess, but this government has done the hard yards to pull the project out of the dirt and deliver the better connections that have long been promised to the Midlands.”

The project was first approved by the coalition government in January 2012 with a £32bn budget for a Y-shaped line reaching Manchester and Leeds, but was pruned back to a single line between London and Birmingham in 2023. Designs for the eventual London Euston terminus are still to be announced.