That, as you say, is a regular 1MΩ 1W carbon film resistor. But 1MΩ is too high to serve any useful purpose in the starter that I can think of, so I am not sure why it is there. However, looking at where the heat shrink sleeves meet the resistor body, there appear to be solid wires poking out with round flat bits on the end or possibly loops, and traces of a black substance. That would have been the Brimistor, a black rod of NTC material between those two ends. They do sometimes crack apart with age.
First, do you need it? Note 1 on the drawing states it is not needed for units below a certain current rating that I can't read, which probably have different contactors fitted. See whether the present application is above or below that figure.
Next thought, Brook Crompton still exist, I'd give their technical dept a call. They might be able to supply one from stock, or advise a modern equivalent NTC to replace it. Brimistors were just one popular manufacturer's range of NTC's, it doesn't have to be a Brimistor.
NTC's are still available and used in various electronic applications. There are a few dozen standard types, that have different resistances, current ratings etc. Much the same as the Brimistors of old, which were sold in a range of ratings more usually targeted at jobs like limiting inrush in AC/DC valve radios and TVs. If we have to, we can select something suitable ourselves.