I have made some progress on the Sunbeam.
After having stripped and cleaned it I was pretty pleased with how it came up. The chrome is in pretty good condition though the paint is a hotch potch with I think very little original paint left. But i will leave that for now as it look presentable.
I cleaned out all the old grease and repacked the bearings. The bottom bracket feels good as do the wheels. The rear free wheel had a lot of grit in it so I pulled it apart also. Pretty simple and I left one shim (out of 4) out to take out a little play. The chain also was full of grit so got a really good clean (shaken in a plastic bottle with degreaser).
I managed to get the chainguard, swing arms, chain and rear wheel back on but I may have to take it off again as it is not very true and it seems to be unbalanced. The tyre and tube are also old though holds air and serviceable for gentle rides. When I tightened the wheel nuts it seized the wheel up and I noticed by backing it off it freed it up again so I added an additional washer between the cone lock nut and the drop out. Still can't quite tighten it enough so may have to go with another washer.
The forks seem pretty ordinary. The drop outs are uneven with one about 6mm lower than the other meaning that the wheel has to be lifted out by that much to get it aligned. It also has a bent tube which means I can't get the head bearings right - loose when straight ahead but tight when turning more than 90 degrees. I will take it to my local vintage bike repair shop tomorrow to see if anything can be done. The gooseneck seems to be a bit bent too so must have been in a bit of a crash.
So it seems like a crappy old bike so far, hopefully I can get it functioning properly and enjoy riding it.
These are some photos from the vendor. Oh, I am not allowed to post photos until I have made 10 posts!