Is it okay to instal white pvc cable instead of grey cable for extra socket?

Are you sure it’s wise of you to undertake this? As by asking questions like this leads me to believe that you might not have the adequate knowledge to carry it out safely. Also, you would have to get some trunking regardless of the colour of the cable, as it has to be mechanically protected.

2.5mm2 cable can be used for ring circuits. It can either be 6242y (grey) or 6242B(white). And can be installed by clicking directly to surface or buried in walls or passing through partitioned walls without conduits. All depends on the protection needed. However, the use of single core cables requires conduits or trunkings as a protection against mechanic damage. It is up to the competent person to detail the method of installation for the client and not the client. Be safe at all times.

If it's BASEC approved it doesn't matter what colour it is

You can use either colour, please ensure its 2.5mm2 if extending the ring

White twin and earth LS0H - Low Smoke Zero Halogen. This is particularly recommended for fire risk areas with the presence of large number of people, due to its excellent fire retardant qualities and reduced fume, toxic and corrosive gas emissions. For fixed applications inside dry or humid environments, or outdoors on buildings and metallic structures. Good resistance to humidity, chemical agents and solar radiation. Whether white or grey it all comes down to your specification.