Opening a UK limited company is at least as straightforward. Registering takes a couple of hours, it can be done entirely online and the fee is £12 ($15). You don't need to be a UK resident. You do need a registered office in the UK, but a company formation agent will provide one for about £20 ($26) per year. All your tax returns can be filed entirely online and HMRC provide a very helpful tax advice service. It really is fantastically simple.
The obvious advantage to registering in Estonia would be the certainty of continued access to the European Single Market. We're still not entirely sure how Brexit will pan out.
https://www.gov.uk/limited-company-formation
https://www.gov.uk/corporation-tax
Another option well worth considering is Stripe Atlas. It's not the cheapest way to start a corporation, but Stripe provide a huge amount of added value.