The contractor only shut three sites during lockdown but is now braced for rising costs and project delays due to new working procedures.
Willmott was speaking after the firm unveiled its latest results for 2019 showing pre-tax profit down to £31.3m from £37.5m last time on turnover of £1.246bn compared to £1.32bn in 2018.
Pre-tax margins dipped slightly to 2.5% from 2.8% and the company ended the year with £93m cash in the bank.
Willmott said: “Our performance in 2019 has provided a good platform for our company to continue delivering projects for customers during the challenges created by Covid-19.
“It’s been a phenomenal team effort from our people as we have adjusted our business to maintain operations during Covid-19.
“Our people quickly embraced the changes required to adhere to the Construction Leadership Council’s Site Operating Procedures, with projects and processes reconfigured to provide a safe working environment for our people and supply chain partners, whose support has been brilliant over the past few months.
“We now expect all sites to remain open, although Covid-19 related safety measures and availability of materials will mean that output levels will be reduced compared to before the pandemic.
“While this will inevitably impact upon pre-pandemic expectations in terms of timescales and budgets, I really appreciate how supportive our customers are being on this issue.
“While we have a healthy forward order book that stands at over £1bn, it’s inevitable that some projects may be delayed or postponed owing to the current economic situation created by Covid-19.
“I think we need to be realistic that output reductions linked to social distancing measures, coupled with a possible lag in the supply of some materials from overseas, will inevitably have a continued impact on project prices and programme timings in the short to medium term.
“We are working closely with our supply chain partners and customers to mitigate this as much as possible, while ensuring that projects starting this year now take into account the likely Covid effect.”