Where did you "push it quite a way down the tube"? In the oil filler opening there's a little metal pipe sticking up that the extractor tube should be attached to. You don't need to push anything down to the oil sump.

 

I believe the 35t has the AJ126 engine.
If so you do NOT push the pump tube down the extraction tube, instead you fit the end of the pump tube OVER the top of the extraction tube.
The point is that you are using a vacuum pump which duh needs a vacuum to work properly and you won't get much of a vacuum if any by sticking a thin tube down the extraction tube.
However if you use the correct plug on the end of the pump tube (IIRC internal diameter of 9 mm) and fit it tightly over the top of the car's extraction tube you will get the desired seal and vacuum and the pump will work well.
I have used this method 5 or 6 times with zero problems and extracted all of the 7.25 litres of oil in the sump each time.
Also you don't need to constantly pump the extractor (mine is a manual pump type), just five or six initial pumps creates a good vacuum and the oil flows out nice and easy, at most a few extra pumps at the end to extract the last few drops.

 

The 35T doesn't have a dipstick with a tube through which you can thread the oil extractor tube.
Instead it has an oil extraction tube accessed beneath the oil filler cap. However, this follows too convoluted route to allow full insertion of an oil extraction tube into it.
Instead, and as designed, you connect your oil extraction tube to the top of the tube under the oil filler cap and that will allow all the engine oil to be extracted.

 

Thanks everyone. As I mentioned, I did my daughter's Audi by inserting the tube down the pipe under the oil fill cap; I assumed the Jag was the same. Thanks again.