 Nokusayina kwaLotus Peter Arundell semumwe waClark kuchikwata che, Spence akapedza nguva zhinji yemwaka wekutanga achityaira mumakwikwi eFormula Two. Zvisinei, nguva pfupi pamberi peBritish Grand Prix, Arundell akatambura tsaona yakakomba mumutambo weF2 kuReims-Gueux, uye Spence akashevedzwa kuti amutsive muchikwata cheF1 kwemwaka wese. Kutyaira zvose zviri zviviri Lotus 25 neLotus 33, Spence akakwanisa kupedza mapoinzi mumakwikwi maviri eWorld Championship, wechitanhatu muItaly uye wechina pamutambo wekupedzisira wemwaka muMexico. Ikoku kwakamupa mapoinzi mana, kuchimuisa akaenzana ne12th muDrivers Championship. 