The finished bike
With new rims, tyres, seat post and pedals. It runs like a dream.

Finally, the bike has a full new life.

Looking down on the final chainline. The 25mm width is a beautiful light tyre with just a little more padding than the 23mm for the London potholes

Showing the back wheel from the other side. The chain is a bit droopy in this picture – but that was easy to fix with an adjustment of the wheel

Back wheel with new rims and tyres. The quick release skewer has been replaced by a hex-key skewer for security
Tyres – Continental Gatorskin. Strong for the London roads and more resistant to punctures, the 25mm width is still light but has more padding than the 23mm to compensate for the London potholes. They aren’t cheap tyres, but the grip and strength given by them over others make it more than worth it.
Rims – mismatch. New rims with screw-on thread for the freewheel are actually quite hard to come by as most rims now fit the cassette systems. I first bought a secondhand pair of Rigida Nova 700C wheels from ebay, only to buy another new rear Raleigh Trubuild 700C rim later due to the following. Can of worms 1: The problem with the Rigida wheels was with their hub – it didn’t exactly fit the current cones and axle. Without a perfect alignment between the cones, the bearings and the hub, the wheel would run badly and could possibly fail. Options included – buy a new hub (pointless because the expense of a) the hub and b) fitting it to the wheel would far outweigh the value of the rim), find new cones that perfectly matched (very very hard to do) or buy a new wheel. I chose the latter. The rims were a part of the bike that, had I planned more in advance how much I would change on the bike, would certainly have been one of the first components to replace as they dictate choice of tyre, choice of singlespeed freewheel vs modified cassette, choice of brakes, and choice of skewers vs axle.
Skewers – Halo Hex Key 6mm. For added security, I replaced the quick release on the front with hex key skewers. Can of worms 2: I thought I could replace the quick release on the back with a hex key skewer, but it turns out that hex key skewers cannot generate enough grip on the frame to prevent the wheel from falling out of the horizontal dropout. The quick release lever can, so this had to stay. It just means locking the back wheel as well as the frame.
Pedals – Wellgo LU 950 Alloy. Though budget, the Wellgo pedals are a vast improvement on the old heavy-duty ones. Lighter and with an improved grip in wet. You can get more expensive pedals, but for a cheap and effective upgrade, these will do just fine.
Seatpost – Valvert single bolt 26.4 x 400mm. A part that is totally dependent on the frame. The width has to exactly match your frame, so make sure you either note the frame width from your previous seatpost or measure it accurately. My frame is a rather unusual 26.4mm, which restricted my choice of post somewhat, but I went for a longer-than-necessary 400mm as the other option would have been too short. Not optimum for weight reduction, but again, an improvement on the old post.

Cones and hubs need to match. In my case the cones on my axle didn’t match the hub, so were incompatible. I had to find another option.