It's easier to explain it by looking at why it happened. Like communism, socialism grew in reaction to the worst excesses of the Industrial Revolution. In the UK the movement already had a root in the independent, self-educated master craftsmen of the late 17th, 18th and early 19th centuries. This sector was notoriously 'awkward', not being of the servant class or the masters, and many of this sector also fostered dissident beliefs such as being against the landed political class, and joining nonconformist religious groups such as methodists, unitarians and quakers.
The 19th century saw industrialisation remove the livelihood of most of these craftsmen, leading to poverty but also to an increase in agitation for political change. Movements such as trade unionism and chartism were the result. Sometimes calls for change resulted in violence, both from the ruling elite (eg Peterloo, 1819) and from the agitators (Spa Fields, 1816).
The movement with the most support was Chartism in the mid-1800s, unfortunately largely sabotaged from within.
At around the same time that the Chartists were losing their way, Karl Marx and Friedrich Engels began formulating an alternative economic system to capitalism, which became communism.
In the UK, a steady improvement in wealth from industry in the later 19th century meant communism didn't gain the follwoing that it did elsewhere on the continent, but nonetheless the generally philanthropic outlook that had its roots in older working and religious traditions continued to flourish, and this became the bedrock of British socialism.
Hence there are still strong links between trade unionism, the notion of a welfare state, and a notion of social equality being 'a good thing', that taken together can be a fair enough shorthand for socialism.