There's not much to a solenoid in terms of wiring, to get wrong.
There will always be a significant voltage drop when the starter motor is operating, so the reduced voltage you see when cranking is perfectly normal. You should with either a resistive wire or a ballast resistor get a voltage of around 9v supplied to the coil, reduced either by the effect of the wire or ballast resistor. The ballast resistor if overheated (this should be suspect if the (green usually) stripe around the black resistive material is burned off - gone - but this isn't foolproof) fails closed, its resistance is reduced. The resistive wire heats less than a ballast resistor does and dissipates that heat safely over a large area, the first thing you need to establish is whether such a wire is present.
A
Take a voltage reading firstly of the raw battery voltage at the battery itself;
B
then with the ignition switched on, take a voltage between a good earth point and the white wire emerging from the bulkhead feeding the coil, when that white wire isn't connected to the coil/ballast resistor, this should more or less be equal to (or be a few 1/10s of a volt less than) the raw battery voltage you just measured at A, if it's significantly less, more than 2v or so less than you have a functioning resistive wire in place and the ballast resistor is probably unnecessary;
C
still with ignition on; proceed by now connecting this white wire to the ballast resistor (noting that it might be redundant) and take the voltage reading through the resisitor, that is on the coils live terminal itself, if the ballast resistor is functioning (they usually fail closed - become less resistive), the voltage between the coil live terminal and earth should again be 2v or so less than that measured at B (excluding a slight few tenths voltage drop as the coil itself is now in circuit, if the points are closed), if the ballast resisitor has failed closed then there should be no appreciable drop from the voltage reading at B;
D
still with ignition switched on; the other wire connected to the coil, not the white but the white/blue should run from the coil to the solenoid, take the voltage between a good earth and the white/blue wire at the solenoid itself, this should be equal to the voltage you found supplied to the coil at C, as as well as supplying the full 12v (less the voltage drop resulting from the starter's load, when it's operating), this white/blue wire harmlessly also does the opposite and the actual voltage received by the coil is redundantly supplied to the white/blue wire and thus the solenoid when the starter isn't turning. The white/red wire at the solenoid is of course the supply from the starter operating position of the ignition switch, which is connected through to the white/blue wire when the solenoid is closed.
Voltage (approximate) at various points.
A (Battery) 13v.
B (voltage in White coil wire feed when unconnected to anything) Same as A if no resistive wire present, say (8-9V) if resistive wire is present.
C (through ballast resistor) at least a couple of volts less than B if ballast is OK
D (White/Blue at solenoid) same as C if White/Blue wire from coil to solenoid is unbroken
Hope this gives you some food for thought. Good luck with it, you'll get there. Oli mentioned something too about the stromberg manifolds two vacuum take offs, one for the dizzy's vacuum advance and another to feed crankcase fumes into the intake system, I wondered if this breather connection was a blocked completely with crud at the manifold end (as they do) or not restricted enough to a pinhole such that it constitutes a huge vacuum leak. I never simultaneously tamper with fuel/carb things and electrical stuff as if anything goes wrong it makes diagnosis incredibly different; electronic ignition kit and a 12V non-cold start coil is highly recommended, for juicy sparks.
Roy, hope you nail it, when you've eliminated the impossible etc. ... It's Viva time!
edited for typos and being just generally garbled.