I don't think they want to do it anyway, they have been lobbying for international cooperation on this and other countries have been dragging their feet. My guess is this is meant to hurry things along a bit.
This isn't like threatening to move offices, which doesn't cost them revenue. The UK is one Amazon's largest markets. Facebook and Google both make billions of dollars in sales in the UK. They're not going to forgo that.
It’s just another sales tax. Amazon already deals with hundreds of different tax rates in different jurisdictions. They’ll just price it in.
Amazon's not always the cheapest as it is. If it prices it in, then competitor's start to look more attractive; which is exactly the point.