Justairports taxi service is the best value option for London to Airports, not sure they will do Oxford, but worth trying them. 

Dunno now but there used to be a direct bus from just outside Queen’s. 

From Heathrow this is pretty good. Not a car but it’s still pretty much direct and very regular from Heathrow.  
 

https://www.theairlineoxford.co.uk/?gad_source=1&gclid=EAIaIQobChMI6ILz…

These are reliable

https://www.001taxis.com/airport-transfers/oxford-to-heathrow-taxis

And if you're calling them, it's justairports.com, not the sponsored (rip off) link which is justairports.london or something. 

Addison Lee will do it and are reliable but Jelly’s link may well be cheaper. Don’t count on finding a black cab at the airport that will do it because they may well not be willing to.  I think for Oxford Uber would probably do it as well but I have never actually tried. 

What Elephant says about the Heathrow Airport - Oxford service from the Oxford Bus Company.  

Thank you Rof you are great. Ok have actionified Jelly's 001 taxi and if they can't do it, one of the other options should get me there. 

Yes it’s a decent service. Drivers good with lots of back up.  Not super posh but can be a bit posh. No boozing and you most of your fellow passengers seem to be into physics or something like that. 

I’d go Uber as I’ve used them for a couple of long journeys from airports.

Surely you have your own preferred private taxi service on WhatsApp. I never land at LHR without it. 

you could get a taxi to gerards cross (23 mins) and then get the train to oxford from there on te chiltern line

Emirates Chauffeur Drive.

I could, Parsnip, but am tight for time this time so I want to go door to door. But am gratefully noting all reccos.