When trying to get insurance, they ask if you have been refused insurance before - what counts as refused?

Having just had renewal declined by our old insurance company, I am confused about how to proceed and get new insurance without risking getting refused again several times and then reducing my chances further! Can I try an on-line comparison site, or is that no point? Part of the problem is that I don't know what counts as refusal. Any advice would be appreciated.

We run our own business and are trying to get a new insurance policy (for public & liability insurance) . Our old insurance company said they would not be offering renewal to us (due to a small claim during the three years we were with them, as our ex-employee cut his hand and claimed, but we couldn't provide a written risk assessment for using a Stanley knife etc.!). Now, we didn't want a renewal from them as they don't cover what we now need, so we were anyway looking for a new insurance company. However, now that we have been refused once, it may be difficult to get a new company as they all ask if you have been refused, and then many refuse to offer quotes if you have been refused. So, if I fill in an on-line comparison site and don't get quoted by most companies does that count as being refused again and now by several companies?! If so, I can't risk trying an on-line site ... Also, do the insurance companies keep a common database of who has refused who, so will they find out of another company did not quote over the internet/through a comparison site?

Or, as I hope, is 'refusal' ONLY referring to a personal refusal by a company, not a generic one simply because they don't deal in our circumstances (eg. having been refused before).