What is required to fly privately from a region with high levels of the ebola virus (Nigeria) to the UK? My dad will be flying us in a private aircraft from Nigeria back to the UK. 

I know that he has been in touch with someone from the UK about this, but since I wasn't present for the conversation I'm not sure what was discussed.

What precautions and declarations should a pilot make when coming from a heavily infected area? We will be landing at a private airport so the current screenings done by major airports will not be considered.
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