As part of the deal, Speedy paid YJL £5.6m and wrote off £1.5m of debt.
YJL chief executive Roger Feast said all five Allen regions, which have a total turnover of £160m, were now making money.
Loss-making contracts are now nearly all completed.
He said: "It was losing cash, but it was a good business with good people by the time we took over.
"We've now got managers going after regional contacts that they can handle rather than large contracts around the country that they could not."
Allen managing director Nick Davies left the group late last year to join Miller Construction. Feast said the five regional managing directors reported directly to him.
He said the Allen acquisition and a number of other deals completed last year would see YJL's turnover reach £500m this year, up from £295m.
It has 11 construction businesses, each with its own brand.
Feast said he would not dump regional brands in favour of one national identity. He said: "Using the brands gives control and ownership to the regional managing directors, and this flat structure works well."