After installing a new dictionary, you need to select that dictionary if you want to use it. In Firefox you choose the spelling checker’s language in a text area’s context menu.
Right click on a text area to open the context menu and select "Languages", Choose the dictionary you would like to use. The "Languages" sub-menu shows all installed dictionaries and includes an item ("Add dictionaries") to install new dictionaries from addons.
Better yet, delete the US dictionary after installing the UK one. To do this, choose Tools and then Add-ons, Select the US Dictionary and press the dictionary's Uninstall button. Then confirm the action and restart Firefox.
Even better! You should have installed a British English version in the first place!