A source said: "This deal opens the way for the management team to start talking to Laing." It is expected to be finalised by August.
The team is understood to have beaten off an offer from fellow niche contractor Killby & Gayford, which is based in London and which has a turnover of about £60m.
The sale of £50m-turnover HWA dragged on in recent months because Laing management had been focused on selling the group's property division, bought by Kier last month. HWA was part of the property division but Laing decided to sell the business separately.