What is required to fly privately from a region with high levels of the ebola virus (Nigeria) to the UK?
You'll be on a flight plan. You'll have to clear customs at a designated airport and file the appropriate paperwork. More info here:

Notification of Flights

If you notify the border agency it will make recommendations if they think your flight poses a risk. There is only screening at Gatwick and Heathrow.

Ebola Specific Information