Is there a Regulation in BS 7671 which gives the minimum distance that a socket-outlet or other accessory can be installed near to a sink?

Answer:

No, BS 7671 does not define a specific distance for such situations. However Regulation 512-06-01 states that equipment should be of a design appropriate to the situation where it is used, and conditions likely to be encountered. In addition, Regulation 522-03-01 states that a wiring system shall be selected and erected so that no damage is caused by the ingress of water. Accessories should not therefore be installed where they may be splashed with water either directly from the taps or by normal use of the sink.

Where splashing cannot be avoided any equipment would require to have an appropriate IP rating (minimum IPX4 or IPX5).