If you have status as a long-term resident in Estonia, which you would normally acquire after five years living there, you can move to all but three other EU countries under the directive 2003/109/EC. See the European Commission's webpage for a brief discussion.
The three countries that have opted out of this directive are the United Kingdom, Ireland, and Denmark, so this will be of no use to you in trying to move to the UK.
Furthermore, if you have not yet acquired long-term resident status, you will have to wait until you have acquired it before you can benefit from the provisions of the directive.