For some strange reason I've not yet fathomed, Khandro, the 'British' version of Firefox sometimes seems to automatically spellcheck whereas other installations require you to install the relevant dictionary first.
If your version of Firefox isn't automatically spellchecking, click the 'hamburger' (three lines, top right) and then on 'Add-ons'. Click 'Extensions', type 'British English' in the search box and hit Enter. The top entry will probably be 'British English Dictionary R1.19 for Firefox . . .' Click the 'Install' button next to it.
Alternatively you might see 'British English Dictionary (Marco Pinto)' listed. I've no idea why different options appear on different computers but, if that's what you see, install that instead.
Spellchecking should then be enabled. If it's not, go to 'Hamburger' > Options > Advanced > General and put a tick next to 'Check my spelling as I type'.