This might sound silly, but I am trying to make one of my characters British and I have a hard time portraying that idea on paper. My novel is set in a fantasy land, nothing like this world and I am trying to make all my characters sound different and unique... any tips or advice?
'British' is a rather broad definition. What place in Britain? What time period? What class? Cockney sounds very different from Received Pronunciation, someone from Yorkshire would sound very different from someone from Newcastle. And don't forget that Scotland, Wales and Northern Ireland are also parts of Britain. First, I would say, settle on an accent and a manner of speaking that are a bit more specific than "British".
Once you've settled on something, notice what makes the speech of that place-class-period unique. It might be expressions that are not commonly used elsewhere. It might be local words, like 'lad' and 'lass' in Scotland. It might be a particular accent: 'cup' is pronounced almost like 'coop' in Yorkshire. (Here's a sample.)
You don't want to go too heavy on the "special" words, or you risk making the text incomprehensible, but you can use them as needed. Accent is the hardest element to represent in writing. You don't want to spell speech phonetically - that makes it hard to understand. But you can mention that a character pronounces certain words in a particular way. You can make it the particular accent of some location in your fantasy world, and make the accent a recognisable trait of the character.
Using the British spelling of words plus some slang would help. I have a character, very American but he spent time in Britain and sometimes uses terms such as ‘twigged to’ instead of ‘realised’.
You can have two characters argue over what the last letter in the alphabet is called - zee or zed.
You can have him thinking he is not the centre of the universe.
I reside in Canada and find the British spellings a bit different still.
Since it is a fantasy, including some of the more common Anglo words might be difficult (lift instead of elevator, flat rather than apartment).
If it were me, I would make his English a bit more formal and use the occasional term not used in American English. I would also have some character or another either remark upon or think that this character has a nice smooth accent and would make the dullest list sound interesting. The reader would deduce that said character is not from the same area as the others.
Try watching some British sitcoms. They'll vary greatly in where they're set and which British accents and dialects arise, but I guarantee you'll encounter something unlike your story's non-British characters. In something like Fawlty Towers, there will be little in the way of regional effects; but with something like Only Fools and Horses, you may need to keep looking things up (especially Cockney rhyming slang), and in anything involving the Scottish or Welsh you might well resort to subtitles.