Some 4000 firms made the 5 December Esos deadline, according to the Environment Agency.
A further 2500 notified the agency that they intend to comply by 29 January, avoiding the risk of enforcement action should they complete and submit audits by then.
Up to 14000 firms are covered by the scheme, which means that only around a third of companies are currently compliant.
The agency indicated it was pleased with progress, given the initial slow uptake, and will now issue reminder notices to non-compliant firms.
While the scheme administrator has the power to impose punitive fines, it has made clear that companies which make efforts to comply will not normally be penalised. The agency recently updated its guidance to encourage companies to submit paperwork even if they miss the deadline
Part of the EU energy efficiency directive, Esos is likely to become a central plank of UK business energy tax policy, currently under review by Treasury.
It requires businesses over a certain size to carry out an energy audit using an approved assessor and have a director sign it off. Firms are not obliged to act upon audit findings. However, given that many companies could easily shave around 10% of their energy costs through low or no cost measures, the audit can provide the necessary impetus at board level to take action.