Proportional Representation would allocate a greater amount of seats and therefore a larger national political platform to fringe extremist parties.
Under the current UK electoral system, it is practically impossible for radical parties to gain many seats. The extremist candidate is usually standing in an area where either Labour, Conservative or the Liberal Democrats stand a strong chance of winning, therefore minimizing the risk of an extremist MP being elected to Parliament despite potentially high national vote shares for the party. For example, the BNP, a far-right, fascist, political party, gained over 500,000 votes nationally in the 2010 election. Due to the first-past-the-post system, they gained a grand total of 0 MPs.
Under Proportional Representation, that number would have been significantly higher.
A study of the 2015 UK election found that if the election had deployed a PR system, UKIP would have gained 83 seats compared to the meagre one it gained.
For those who view UKIP as a radical xenophobic party, this would have been a negative outcome.
A further study carried out at the Harvard Kennedy School of Government also drew a link between PR systems and the way they benefit radical, right-wing parties. 
The study showed the historical link between the PR form of voting and the way it supported extreme parties gaining a foothold.