Can I use the shaver socket in the bathroom?

Yes, they can be located in zone 2 (or beyond) according to the IEE Wiring Regulations defining zones for electrical equipment in bathrooms, providing they are unlikely to be the subject of direct spray from any shower.

Please note this information is given for guidance only, always refer to the current IEE Wiring Regulations or a qualified electrician to ensure that you are guided by the latest regulations/code of practice.