we used Lingfield Racehorse Transport to goto Towcester pony racing recently - nice drive, good Theault lorry, very good round roundabouts and corners and very clean, tidy and helpful
would recommend and the horse would have a good drive and surprisingly one of the two cheapest quotes we got but as a new lorry makes good time on good roads without being driven stupid.
although he's not in Cornwall or Oxford I'd still give him a call - google will find the phone no. as i've not got it on me
p and l luck 01579345151 also i know that cherrytop stud at devon do shared loads if they are off up the country to collect anything. also there is claire howarth in devon 01271-858583 all collect from cornwall most weeks
I have used P&L Luck a few times and they are great and I will use them again when we move in a couple of months' time. They are based in North Cornwall but are up and down the country all the time and Oxfordshire would certainly be no problem for them (we used to be based in Berkshire).
I used Julie Magnus horse transport to take my 2 weanlings from Hampshire & Bedfordshire to the East Midlands, and she was fantastic. She transports all over the country and i would recommend her to anyone... really lovely lady!!