I think the health impacts are made clear, and I suppose we can make that choice.
But there's another issue about protecting our own chicken farmers and their industry, because they could be caught between a rock and a hard place if chicken produced using cheaper methods floods our market. I had a google, and discovered that we produce 60% of the chicken-meat sold in the UK, whether fresh or frozen. So if our chicken farmers want to compete with the US chicken they might be forced or encouraged to change production standards and start providing chlorine-washed chicken to the UK market themselves. However, the British market mainly wants breast, but the dark meats of the leg, thigh, wing are less in demand and these primarily get exported overseas. 75% of those dark meat exports go to the EU, around £170 million-worth of exports. If the British producers want to keep exporting this dark-chicken meat to the EU they will have to conform to EU standards, i.e. no chlorine- washing.
So, a chicken farmer might have to face either losing out on breast-meat sales within Britain to cheaper-produced US imports, or losing out on dark-meat sales to the EU.
What? The UK keeps the dry boring part and sends all the tastiest bits over to the continent? I have no idea why they think we have shit food.