You Do Need power plug adapter while traveling from Solomon Islands to United Kingdom (UK).

Here is Why You Need An Adapter

The outlet and plug type used in United Kingdom (UK) is G and in Solomon Islands are G and I. This is how they look like.

Solomon Islands

In Solomon Islands, outlets of type G and I are in use.

Type G

Type I

United Kingdom (UK)

In United Kingdom (UK), outlets of type G are in use.

Type G