This is after construction output fell by 2.9% in December 2020.
However, the level of output in January 2021 was 2.6% below the February 2020 level.
In addition, the level of new work was 6.4% below this level, while repair and maintenance work was 4.5% above this level despite a monthly fall.
New work increased by 1.7% in January 2021 and was accountable for an uplift in private commercial and infrastructure, which grew by 4.5% and 3.1%, respectively.
Repair and maintenance declined by 0.4% in January 2021, which was due to a 4.7% fall in private housing repair and maintenance.
This drop is despite growth of 5.0% in public housing and 1.3% in non-housing repair and maintenance.
Looking at the data on a quarterly basis, construction output grew by 1.7% in the three months to January 2021, compared with the previous three-month period.
This was accountable to growth in both new work up 2.2%, and repair and maintenance rising by 0.8%.
Paul Fenner, head of construction at BDO, said: “Construction output suffered a minor blip in December 2020, but the latest figures for January 2021 show that the sector’s recovery is back on track.
“The more positive figures reflect a growing confidence among construction firms that the worst is behind them.
“Indeed, BDO’s latest survey shows that 85% of construction firms are feeling positive about their prospects for the year ahead.
“However, risks remain and firms will need to keep a tight rein on costs and maintain strict financial discipline as we enter a very uncertain period.”