Richard is correct, the radiator is removed from underneath. Believe me Niels, I have done this on my 1976 Plus Eight car a number of times.
You don't need to remove the cowl, neither any 'cross members'. I trust that the 'cross member' that you refer is the inner-wing or valance tie-bar that supports the radiator. Be careful to site it back in it's original position otherwise you'll find your cowl shape will change and your bonnets won't fit as before.
To remove the radiator, jack up the front of the car and put on axle stands; loosen the four nuts and bolts holding the two radiator mounting plates to the front suspension crossframe so that they can be swung out of the way. You can also undo the bobbin nuts but leave everything suspended on the mountings.
You will need to remove the steering tie bar that links both front stub axles but probably not the draglink from the steering box. Loosen the draglink block on the steering tie bar and loosen the steering joint nuts at either end half a turn remembering that one side has a R/H thread, the other a L/H thread. On reassembly, you want it get this back in exactly the same position in order to avoid to have the car's toe-in adjusted.
Spin the steering tie-bar until the steering joints and tie-bar are free from each other and swing back out of the way of the radiator bottom outlet.
Now carefully lower the radiator remembering that it is a heavy piece of brass and copper and you don't want to drop and damage it. Better done with two people just in case.
The original Wood & Jefferies fan was never really up to the job and a Spad will be a significant improvement. As for mounting it: as close to the radiator as possible; consider soldering some four small mounting plates to the side of the radiator.
Finally, and some people may take issue with this, oil plays a bigger part in removing heat from the engine than the water does. Others are convinced that the water is what primarily cools an engine. Think about it: all that friction going on in the cylinder walls, crankshaft, etc, etc. All that hot oil gets simply dumped in the sump to be recirculated time after time around a hot engine. I'd recommend fitting an oil cooler (13 row possibly 16 row) using a sandwich plate between the oil pump and oil filter. The oil cooler can be mounted under the cowl box using some suitable brackets.
I trust that this helps.
