For a short version of the history GB, see
https://en.wikipedia.org/wiki/Velocette_LE.
And I see Rog has just come back on this too, as I was typing . . . so apologies for repetition but I've hammered it out now!
Basically, conceived as a post-war commuter bike for Everyman - and Woman, very much so - the LE ('Little Engine') was big gamble that never really quite paid off. Idea was to revisit the two-wheeled car thing really, with quiet running, weather protection and all that. A big-wheeled scooter some might say, but really it's not. Luckily the Police took loads of them, over half the production in due course, and that led to a lot of good upgrades including 12v electrics to power radios etc. Civilian ones stayed at 6v though - both mine were/are - with flywheel alternators with three lighting coils and a pair of 3v HT coils in series (usually ditched in favour of a wasted spark double-ender, which is far cheaper than rewinding the originals)
They started with roller big ends and 150cc, plus BTH dynamo electrics, then went to 200cc with plain bush non-split big ends (steel rods), loads of bits of bronze everywhere in fact to support crank, reduction gear shaft for the clutch etc etc. And Miller ac electrics which are actually pretty darn solid.
Loads a bits on the inside, all quite fiddly, with quite a bit of plumbing for the lubrication system. Accessibility is not a strong point for non-routine maintenance, no Sir, but to be fair they don't need much once they're up together. The last ones were made in 1970/71 and they were in use by police units for a few years after that. I used to compare notes with a local Hampshire policeman now and then when I had my first one.
The open-frame flat twin you mention was the air-cooled Valiant, launched in 1957 (so 9 years after the first LE) with two carbs and a rather more sprightly gait plus a classic 4 stroke noise. It had a heady 12bhp with overhead valves and a high compression ratio (well, 8.5:1 instead of I think about 7 on the LE). Same general idea but looked like a 'proper' bike, very pretty in fact, a small Duggie almost some might say (without meaning to insult another great marque!). Valiant engines have been put in LEs to create the odd 'Leval' - and there is even one LE running (I think it is running, anyway) with an electric motor.
The net net of it all was the factory got into a financial pickle, blamed by some on the LE programme, but probably coming anyway. I think they made a loss on the bulk sales, as the bikes were obviously expensive to make compared to a typical Villiers-engined lightweight or a Bantam, and were priced well above the norm for lightweights for civilian buyers. Presumably heavily-discounted for the police. But many many thousands were made across the 22-odd years they were current in their three different Marks.
The positive consequence of the Police sales was that there were gazillions of spares in lots of police workshops, which were snaffled up in the early days of the owners' club and saved for the future owners, quite a few of whom are even today former police officers who developed some bizarre form of fondness for the things. I got one when I was 15 because what else can you get for a £1 out of the cellar of one of your dad's mates ready for the Big Day when you were 16 and able to go places legally?
Not knowing any different, I found 'proper' bikes a bit startling when I discovered that 'acceleration' meant more than 'lean forward gently' - oh, and that other bikes also broke down quite a lot. But, as a 16 year old, it was transport, it was MINE, it was very reliable and it meant I could get jobs on building sites etc in school holidays outside the village and generally pretend to be a grown-up and get to the pub. Must have done a good few miles on it, and it never broke down, ever. Sold it in the end for £7.50 - SLT 310 where are you now I wonder? If you're out there I'll have you back any time . . .
