That plug lead should screw into the plug cap quite a long way. It is difficult to tell how far inside it is seated, but I marked one of mine with felt pen before I took it off a few years ago - it was about an inch. A felt pen mark an inch from the end of the HT lead before you start to screw it in will help to inform you of how far to screw it in. A little silicon lubricant on the end also helps. The HT lead shouldn't normally just come loose - unless the PO tried to just push it on (like you have to at the coil end - but that has a gland to keep it secured), OR the copper core of the wire is corroded. If it is - it is very obvious - there will be visible signs of light green copper oxide - Verdigris - in the core.
Pictures show (1) the marked HT lead and the depth to which it was screwed into the plug cap; (2) the coil end of the HT lead with the glued on grommit, the tiny washer and the gland nut. Again, it goes into the coil a long way - but this end is a push fit.
it is possible to use bog standard copper cored HT lead, but the OEM part comes with an additional outer sheath, and that all important glued-on grommet. An alternative to the grommet needs to be found for a replacement lead which can be secured to the HT lead - as it is only this that keeps the HT lead firmly located in the coil. That tiny washer allows the gland nut to be tightened without twisting the grommet.