NOW then. Now then. Then now. Now then...

What's going on here?
Firstly, I think you'll find that being in the middle of the map at the top, where God put us, makes the British normal.
Its the rest of the world that is wierd.
And, since we decided to stop running it for a while, that world has become increasingly wierd of late...

Hehe...
How to make the British wierd eh?
Well, i think you'l struggle to top the reality of the British war effort, what with Barnes Wallace and Maj Gen Percy Hobart on our team.
http://en.wikipedia.org/wiki/Hobart's_Funnies 
However, i'll echo and recap the excellent suggestions made so far.
The Once and Future King (Arthur Pendragon) is certainly a way to go really wierd...especially if rules-wise he 'inspires' the British troops to put down their SMLEs and pick up a longsword for a glorious mounted charge...
Our climate is 'foggy, raw and dull' (according to the French in Shakespeare's Henry V) and is definately a supernatural mine of wierdness. Mist-revenants, trolls under bridges, Cornish giants, witches and wise-folk, brownies, sprites and assorted forest spirits (including the elf-kind of the Seelie and Unseelie court) are all possible allies that could be brought forwards.
Technologically speaking...well...i refer the honourable gentleman to Hobart's Funnies...Also a browse through the world of Heath Robinson is highly reccomended.
In general, British technology, and our relationship to it is at best by casual acquaintance. A walking tank is all very well, but nothing beats 'a bayonet with some guts behind it'.
Rules?
Well, the teabreak is vital. British troops should be able to call a tea break that restores their morale, and stops the fighting for a while (foreign types can spend the time doing whatever it is they do when they should be supping a mug of hot milky tea (digestive biscuit optional)).
Stiff upper lip. The British unwillingness to look facts in the face, or to admit defeat; and their ability to disregard, denigrate and generally feel superior too and sorry for foreigners should definately give them the ability to shrug off panic, worry, morale failure and in many cases bullets.
Getting stuck in. One thing the British do well is 'get stuck in' to problems. Don't get me wrong, we think things through beforehand - usually to an illogical conclusion....but nothing beats getting stuck in for actually achieving things. How else do you think we built an Empire? British units should be able to act where others couldn't (during suppression for example). Of course, this capacity to act is somewhat compromised when we're 'getting stuck in' to a teabreak.
Cricket. The sport of Empire, and the ultimate test of colonial manners...(some of them are dashed rude).
Also a cracking good chance for a 'gentleman' to show his worth in the face of profession 'players', proving once and for all that breeding, good manners and an amateur expectation of superiority will always beat skill and competence. Of course being a jolly good chap at the crease is also handy for knocking grenades for six...
The mad minute. British naval and army fire discipline has always favoured 'rapid, accurate fire'; a doctrine that led to the sinking of HMS Hood, and to the Old Contemptibles of WWI giving the Germans the impression they were facing machinguns.
Being ammunition-hungry, this rapid fire in the army was restricted to 'the mad minute'. See...thinking it through and getting stuck in...
This desire to conserve ammo is why the MOD refused to issue our chaps with assault rifles until 1985...(41 years after pretty much everyone else)...
So, the British should have a ratherwierd capacity to lay down machinegun fire with anything at hand (bolt action rifles, pistols, longbows, thrown stones, etc.)
Ooh...longbows!!!
Yeah, got to have something wierd to do with longbows...