The NHS has already opened 63 long Covid clinics to try and offer help to people who have suffered for months after their infection.
There will be 83 clinics open by the end of the month.
As he announced further investment in the clinics, Sir Simon said there will be “at least one” clinic in every local health area – also known as an integrated care system (ICS).
Figures suggest hundreds of thousands are suffering several months after their first infection.
Speaking to a Health Service Journal leadership event, Sir Simon, chief executive of the NHS in England, said: “We want to make sure that the health service continues to expand its offer for long Covid.
“To that end we have 69 clinics identified last year, we will have 83 long Covid clinics in place by the end of this month, so a significant expansion there.
“There will be at least one service in every ICS area.
“We will be backing that with at least £24 million earmarked revenue funding going into this new financial new year up from the £10 million which was announced last year, and there will be more to come.
“We’ve got to make sure that there’s a clear front door for people who need that assessment.”
Results from the latest Office for National Statistics coronavirus infection survey suggest more than 600,000 people in England experienced long Covid more than 12 weeks after the first suspected infection with Covid-19.
There are a wide range of common long Covid symptoms including fatigue, shortness of breath, chest pain or tightness, problems with memory and concentration, insomnia, dizziness, pins and needles, joint pain, depression and anxiety, tinnitus, earaches, feeling sick, diarrhoea, stomach aches, loss of appetite, a high temperature, cough, headaches, sore throat, changes to sense of smell or taste or skin rashes.