The ICS said applications for compensation could be considered even from those who failed to win awards out of earlier arbitration hearings against the firm.
More than 300 former Knight Williams investors did not go through the arbitration scheme available through the company's former watchdog, Fimbra.
They can already apply for financial redress from the ICS, as long as they prove that they were poorly advised by Knight Williams sales staff. Up to 70 more Knight Williams clients who went through Fimbra's arbitration scheme lost their cases, often because their claims were not properly set out, even though they had lost money because of bad advice.
They may still be able to claim compensation from the scheme, but will have to show the basis on which they are applying is different from their earlier complaint to the arbitrator.
David Cresswell, client relations manager at the ICS, said: "We have had problems with arbitration awards in the past. Our legal advice has been that they are binding. The arbitration award, or the refusal to award one, extinguishes the civil liability to an investor.
"What we therefore have to do is to see whether the claim that the investor is making can be classed separately."
Mr Cresswell warned that the ICS would not be giving priority treatment to Knight Williams savers: "The matter will be speeded up by the fact that the firm has gone into liquidation and claims were already advanced, but we have another 193 firms whose former clients are in similar circumstances to those at Knight Williams."
Had the firm not gone into liquidation this week, many savers would have received some compensation within weeks under plans agreed in November last year.
In a separate move, the Securities and Investments Board, the City's senior financial watchdog, wrote to investors yesterday telling them it would pass all the information it could to the company's provisional liquidator, Arthur Andersen.
Kenneth Jordan, a leading member of the Knight Williams Investors Action Group, said: "This is the best news that I have heard for some time. I had said to the ICS that legally, even if a person had lost one case before the arbitrator, there was nothing to stop them arguing another when it came to the compensation scheme. They appear to be confirming this."