Diesel: 118.83p/L divided by 35.8 MJ/L equals 3.32
Petrol: 113.29p/L divided by 34.2 MJ/L equals 3.31
Vegetable Oil: 100p/L divided by 33 MJ/L equals 3.03

https://en.wikipedia.org/wiki/Energy_density
http://www.theaa.com/newsroom/news-2015/aa-fuel-price-update-april-2015.html
http://www.tesco.com/groceries/product/search/default.aspx?searchBox=vegetable+oil+5L&search=Search&N=0&Nao=20s

Petrol is a little cheaper than diesel.

Petrol can be blended with ethanol.
Bio-diesel is created from oil and methanol.
Diesel cars can be converted to run on pure vegetable oil.

Which is cheaper?

It depends if you actually upgrade your diesel car to vegetable oil.