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Yes, that's the blue that was underneath. Had to do some touching in in parts, but overall the acetone worked a treat with a microfibre cloth. Took some patience to do but well worth it. The front shifter is a bit tricky to set up yes, but I've used it before on my Ellis Briggs and I find it really easy to use, so thought I'd put it on here (whilst the Ellis Briggs is on baby carrying duties running a 3 speed AW hub).
You are right about the chain though, the wheel does definitely need setting forward in the dropouts-I'll have to try and remember that before using it this week.
The top tube is a weird one, it has a definite bend down into the lug when you look at it, but having stripped the paint in that area there is absolutely no sign of creasing, stress fractures or crash damage at all, and the forks and down tube are not bent in any way. The bend is not as bad as it appears to the eye, maybe only 1-2mm maximum when you set a level on it, and the bike feels fine to ride when I've tried it (over admittedly short distances), so hopefully all will be well and I won't be going head first into the road due to tube failure...!
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I wouldn't worry too much about that bend, but I suspect it is crash damage.
My main point was, once again, that if you have anything made in imperial measure, it's best to stick to that system - conversions will only lead to inaccuracies and trouble. Your frame will have been made to some round number of inches between the centre of the rear fork end and the centre of the front fork end - if it doesn't come to a round number (possibly including half inches) something is bent.
North London Veteran - Cycle Club Rides
I notice you live in Chingford - the NLVCC rides usually meet in Hertford, which would be pretty convenient for you. Your Gillott would be a typical bike for that group.
There is a regular ride on the third Wednesday of each month - I realise you are young enough still to have to work, but there are some weekend rides. You would not need to join the VCC to start with, but you should have third party insurance to go on any ride with any club (or any ride at all, really) Let me know if you're interested and I'll keep you posted.
Is that the blue finish that you have recovered from the white overpainting? If so you've certainly done a good job.
Those Simplex front changers are a bit more tricky to adjust than later versions and they're a bit on the heavy side, but I note the French pros went on using them well into the 543 era, so they must have something going for them.
One small point: the chain looks too short, but the back wheel is as far back as possible in the fork end. This is not how those long ends are intended to be used with gears - they are not like vertical drop outs! If you just bring the wheel forward so it's about the middle of the slot I think you will find everything looks and works a bit better.
If you now use an imperial tape measure and look at the distance between the front and rear spindle centres, I bet you will find it's either 40, 41 or 42" which would have been a normal wheel bases for this type of frame. (This is assuming the top tube isn't bent).