Can't remove crank on Raleigh Equipe
Everything looks right. Whenever using a crank puller but especially when it's taking a lot of force, it's very important to have the tool installed into the crank arm with some real torque, not just finger tight and never loose. You can grease the threads if there's roughness. Here with the nutted spindle it's a good idea to start with the puller either in two pieces like you have it or at least threaded far out, so you know the tool is getting torqued into the extraction threads and not getting bottomed out against the spindle tip. Once it's in there tightly you can use a lot of torque on the business part of the tool.

Square taper cranks are a press fit and so by nature, penetrating oils and the like usually won't do much to help loosen them. That is to say, putting whatever amount of force through the tool that's needed to do the job is all anyone can really do to remove them. There are other methods when extraction threads fail, but they tend to damage cranks anyway.

If getting enough leverage off the other crank is the problem, you can either rest it so it's torquing against a stationary object or take the pedal off and put a piece of PVC over it for a non-marring cheater bar.