The busy road's being made two lanes in both directions between Segensworth and Titchfield - it's due to take 18 months.
Hampshire Man In McGrath Murder Trial
The trial of a Hampshire man charged with murder after a 32-year mystery surrounding the discovery of a young woman's body near Peterborough is underway.
Sally McGrath, 22, was found naked in a shallow grave in woodland in March 1980 after vanishing in July 1979.
Despite what police describe as Cambridgeshire's biggest pre-Soham murder investigation, the killer could not be found.
Last year, Paul Barry Taylor, 60, originally from Peterborough and now living in Fareham, was charged with the murder.
Taylor also faces three counts of rape, one of serious sexual assault and one of indecent assault against three different women.
The former builder and chip shop owner denies the charges.
Miss McGrath was last seen alive at about 3pm on July 11 1979 at the Bull Hotel in Westgate, Peterborough.
Her body, naked except for a pair of boots, was found by a gamekeeper on March 1 1980, partially buried in Wild Boar Spinney, at Castor Hanglands, to the west of Peterborough.
A post-mortem examination revealed she had died from a ''blunt force'' injury to her head. Miss McGrath had been living with her parents and brother in Towler Street, Peterborough, when she vanished.
Prosecutor Karim Khalil told Chelmsford Crown Court on Friday 12th October 2012 that Taylor was married at the time of the 1979 offences.
He openly slept with other women, regularly going for ''quickies'', but insisted in a police interview that the relationships were always consensual.
But Mr Khalil said:
''In the 1970s he was a reasonably good looking and physically strong young man. He was brimming with confidence and had the capacity to be an engaging flirt and a ladies' man. ''But if he did not have his own way he had the capacity to become violent very quickly. He used this violence to force young women into submission or simply have his way with them.''
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