The Queen and Prince Charles can veto bills that affect their interests
Before parliament can debate a bill that's likely to affect the “hereditary revenues, personal property or other interests” of either the Queen or Prince Charles (in his role as Duke of Cornwall), their explicit permission must be obtained.
Whitehall papers show that overall at least 39 bills have been subject to this process, known as "Queen's consent" or "Prince's consent". We don't know how many bills have been amended or vetoed altogether before reaching Parliament.
Official legal advice makes clear that the Queen's and Prince's consent is not a mere formality. The process by which consent is obtained, which includes consulting with the royal household and seeking legal advice from its solicitors, provides a clear opportunity for the Queen and the Prince of Wales to influence the shape and content of a bill before it reaches Parliament.
NB. Queen's Consent and Prince's Consent are quite distinct from Royal Assent. Royal Assent is granted after a bill has passed both houses of Parliament, whereas Queen's Consent and Prince's Consent are granted before a bill has been introduced to Parliament.