I cannot see where on that site one can find tephigrams or any other UKMO 3D data.
Well, being only a tv producer and not a forecaster, I didn't actually know what a tephigram is - but luckily tv producers have to be good researchers as well, and this particular one also happens to have spent some years working with a group of high profile Met Office forecasters. So, is this what you want -
http://www.meteo.uni-koeln.de/meteo.php?show=En_We_We - I found the the current British data and much more by following the links under "Radiosonde data"
I'm not sure of the point of obtaining raw met data. The big organisations use the largest computers in the world with a room full of PhDs writing incredibly complex program to run on them and they still can't get it right some of the time. What chance does a PPL have from looking at pressure and temperature data at a few places in the UK?
What you can do is what the forecasters do - look at the output of the various models, which can be found at my earlier offering of Wetterzentrale, and try and make an educated guess at what is actually going to happen. Of course the average PPL has a few hours of education and the pros have a lifetime - but what the hell, it's a prediction.....
B