If a US bounty hunter tried to grab someone in the UK they could be charged with 'false imprisonment'. Obviously if they did attempt to "BRING YOU BACK BY FORCE" (sic), then they could also be charged with GBH, assault etc.
If there was an Interpol red notice for the suspect then they could be arrested by the UK police and would face extradition proceedings, but in general, the only people that can arrest people in the UK are the police.
tl/dr US bounty hunters have no jurisdiction outside the US.