While I cannot predict the specific actions of law enforcement officers in a hypothetical scenario, I can provide some general information. In most countries, the law applies to everyone equally, regardless of their social status or position. If Queen Elizabeth II or any other individual were driving and exceeded the speed limit, it would typically be within the jurisdiction of the police to issue a fine or take appropriate action.
However, it's worth noting that in some countries, certain high-ranking government officials or dignitaries may have certain legal immunities or protocols in place that could affect how such a situation is handled. These immunities or protocols vary by country and may afford special treatment to individuals in positions of authority. For instance, in some cases, the authorities may choose to handle the matter discreetly or through diplomatic channels.
Ultimately, the specific outcome would depend on the laws, regulations, and protocols in place in the particular jurisdiction and the discretion of the police officers involved.