I think doing it in a home-built would be true to the spirit.
Indeed jon Johannson has managed two circum-navigations in his RV-4, both E-W and W-E. He also made use of Polly Vacher's fuel in Antartica, when she was unsuccessful in crossing that continent recently (I hesitate to call it a failure). Last year a guy flew his homebuilt around the world from Gloucester attempting a speed record, which sadly got spoilt by a week of bad weather keeping him in Hawaii, but several other records were broken en-route.
The planning for these trips is a horrendous task, and , in theory, the day/vfr restriction of UK permit aircraft would rule it out for the Cape-Town record. In principal though it is achievable on a 160HP homebuilt and plenty of determination.