Yes you can proceed and apply to a bank that is part of the Help to Buy scheme.
They will however take your credit rating and history into account as they would if issuing a normal mortgage loan. So a bad credit rating might be a problem and prevent a successful application.
It is always good to use credit checking websites like www.experian.co.uk or www.equifax.co.uk before you begin an application. This will give you a full credit report including any historic issues and sometimes rectify them if they are incorrect.