Any email from websites or services that you normally use that ask you reply or click on a link to enter your personal details, including your password or bank details, are fake emails from phishing scams.
You will never receive an email from the Lit & Phil asking you to enter your bank details or your username and password for the website. If you have any issues with your password, you will only ever receive a reset link to your email so that you can set a new one after you click on the 'Reset Password' link on the login page. This email will be sent from website[at]manlitphil.ac.uk and will contain a link with the URL starting with 'https' [the 's' is important as this means its a secure website]. This link will then take you to the Lit & Phil website where it will authenticate your login with a one-use set of credentials so that you can then set your own password.
PayPal is a third party service used by the Lit & Phil to process online payments. The Lit & Phil do not store any of your PayPal login or bank details. All of the information you provide to PayPal will be securely stored by PayPal itself. If you receive an email purporting to originate from PayPal that asks you to click a link or reply to the email with any personal details, including bank details and username-password information, this is a phishing email. PayPal will never send you an email asking you for these details, even if the email claims that there is a problem with your account or claims that your account has paid for items without your knowledge. When you first set up your PayPal, you choose a series of security questions that only you know the answer to. If you ever have to change or enter your personal details into PayPal, such as change your password, you will be asked these security questions in order to determine that it is genuinely you who is requesting a change of details.
For more information about how to spot a phishing email, you can read this article on the PayPal Frequently Asked Questions: "How can I tell if my email is genuinely from PayPal?"