This is the key conclusion of an analysis by consultancy Cornwall Energy.
The LCF sets a cap on spending under the Renewables Obligation (RO), feed-in tariffs (FITs), contracts for difference (CfDs) and investment contracts (an early form of CfD approved before the current regime was established). The LCF budget indicates what can be spent on low-carbon energy without affecting consumers' bills.
Increased spending would come despite sharp cost reductions to renewable energy subsidies from 2015 and an early end to onshore wind under the RO. These have led to investor uncertainty in the UK and a reduction in the project pipeline.
Cornwall's analysis suggests cost controls on renewable energy have almost brought projected spending back within agreed figures.
The figure for 2020/21 would only exceed the LCF target by £100 million (€129 million), far less than that projected by the Office for Budget Responsibility in July, ahead of rollbacks in renewable support.
Even so, the analysis foresees an average increase of 13% a year, from £4.2 billion (€5.4 billion) in 2015-16 to £7.7 billion (€9.9 billion) by 2020-21. This would lead to an overspend every year from 2016/17 to 2020/21.
It concludes that, in each year from 2016-17, spend will exceed the LCF and require some of the contingency budget by as much as £0.6 million - or 51% of the contingency - in 2017-18.
Cornwall Energy says the annual increases are frontloaded, so that they rise 18% from £4.2bn to £5.0bn in 2017-18, and then by a further 24% to £6.2bn in 2018-19.
A key cause of the price hike is an overlap between the last phase of the RO, ending in 2017, and the start of payments for the first CfDs.
A further reason for increased pressure on consumers stems from the Department of energy and climate change's (Decc) decision to bring forward the capacity market by a year to 2017-18 to deal with growing concerns over energy security.
For its part, Decc says early introduction of the capacity market will avoid price spikes from coal plant closures and maintains that cost controls have saved consumers £30-35 per year from 2014 and continuing out to 2020.