The app may not be accepting your password for one of a few reasons. The most common reason is because there are 2 ways to subscribe to the app: directly through https://subscriptions.independent.co.uk/, or through the App Store on your device.
If you are subscribed directly through iTunes, Google Play or Amazon Kindle you can reset your password by visiting the following website:
Apple iTunes: http://iforgot.apple.com
Google Play: https://www.google.com/accounts/ForgotPasswd
Amazon Kindle: http://www.amazon.co.uk/gp/help/customer/display.html?nodeId=201168590
If you are subscribed through Independent Subscriptions you can reset your password by opening https://subscriptions.independent.co.uk/ in a web browser and then click on 'Sign In', then 'Forgot Password?' and enter your email address. You will then be sent a message that contains a link to reset your password.