The government has awarded £6.6bn in contracts to build the new high-speed railway between London and Birmingham, to companies including crisis-ridden construction firm Carillion.

Construction work is due to begin in earnest next year on new stations, tunnels, embankments and viaducts on the London to Birmingham line, which forms the first phase of the controversial HS2 project.

The major infrastructure project is expected to create 16,000 jobs, with the first trains due to run between London and Birmingham in 2026.

Chris Grayling, the transport secretary, is due to update MPs later on Monday on phase 2b of the HS2 route between Crewe and Manchester and from the West Midlands to Leeds.

Grayling is expected to confirm changes to the final route for the Y-shaped second phase to Manchester and Leeds, including alterations to the original proposed route around Sheffield.

Plans for a dedicated HS2 station at the city’s Meadowhall shopping centre were opposed by city councillors, and it is expected that the line will follow the M18, with a slow rail spur into the city centre – despite the objections of affected residents and local MPs, including Ed Miliband.

Critics have warned this will mean homes on the new Shimmer housing estate in nearby Mexborough being bulldozed. Some residents found out about the HS2 plans just weeks after moving into the development of two- and three-storey townhouses.

Grayling will also publish a bill to prioritise phase 2a of HS2, which involves speeding up construction work between Birmingham and Crewe.

Opponents of the high-speed rail scheme claim the government is drastically underestimating the true cost, and that construction has already been delayed. The overall budget was revised up to £55.7bn, but estimates drawn up earlier this year on behalf of Lord Berkeley, chairman of the Rail Freight Group, who had argued at select committees for alternative routes for HS2 out of London, suggested it could be as high as £111bn.

Carillion’s joint venture with French construction company Eiffage and UK firm Kier has won two contracts worth £1.4bn to design and build the North Portal Chiltern tunnels to Brackley and the Brackley to Long Itchington Wood Green Tunnel South Portal.

The troubled construction company’s share price crashed 70% last week after it issued a profit warning and announced the departure of its chief executive. However, Carillion shares were up more than 8% in early trading on Monday after the HS2 contract win.

Balfour Beatty’s joint venture with French firm VINCI has won two contracts worth £2.5bn. They will design and build the Long Itchington Wood Green tunnel to the Delta Junction/Birmingham Spur and the section from the Delta Junction to the West Coast main line near Lichfield. VINCI has been involved in the high-speed Tours-Bordeaux rail project in France.

The Balfour Beatty chief executive, Leo Quinn, described HS2 as a “generational engineering project”.

Other companies to have won HS2 work include Costain, Sir Robert McAlpine, Sweden-based Skanska and Austria’s Strabag.

A venture between Skanska, Strabag and UK firm Costain, which has worked on Crossrail and the Channel Tunnel, won contracts worth nearly £2bn.

HS2 phase 1 construction contracts

Area South

S1: Euston Tunnels and Approaches – SCS JV (Skanska Construction UK Ltd, Costain Ltd, Strabag AG)

S2: Northolt Tunnels – SCS JV (Skanska Construction UK Ltd, Costain Ltd, Strabag AG)

Area Central

C1: Chiltern Tunnels and Colne Valley Viaduct – Align JV (Bouygues Travaux Publics, VolkerFitzpatrick, Sir Robert McAlpine)

C2: North Portal Chiltern Tunnels to Brackley – CEK JV (Carillion Construction Ltd, Eiffage Genie Civil SA, Kier Infrastructure and Overseas Ltd)

C3: Brackley to South Portal of Long Itchington Wood Green Tunnel – CEK JV (Carillion Construction Ltd, Eiffage Genie Civil SA, Kier Infrastructure and Overseas Ltd)

Area North

N1: Long Itchington Wood Green Tunnel to Delta Junction and Birmingham Spur – BBV JV (Balfour Beatty Group Ltd, VINCI Construction Grands Projets, VINCI Construction UK Ltd, VINCI Construction Terrassement)

N2: Delta Junction to WCML Tie-In – BBV JV (Balfour Beatty Group Ltd, VINCI Construction Grands Projets, VINCI Construction UK Ltd, VINCI Construction Terrassement)