I am interested in the articles of association and shareholder's agreement of a UK company. Where can I find them?
The UK Government is trialling free data access to the Companies House register. Go to the beta website, search for the company's name, click on the heading with the corresponding company, then click the "Filing history" tab. You can see Incorporation, appointment of directors, and annual returns.
Previously, the way to access the records was through Companies House Web Check and cost £1 per document. Enter the company's name or company number and click "Search", which takes you to a spreadsheet. Find the right row and click on the company's number in the leftmost column, which takes you to the company's record. Click on "Order information on this company". Check the boxes of the documents you want and add to order.
Source for the previous way: JustAnswer.