Hi,
With one day you really are left with the Interstate route Tim suggested unless you want an extremely long day.

Now with 2 days [and being from the U.K myself, I would highly recommend finding the time] you will be in for a treat. Both options previously mentioned are great, and again if you can give yourself the time Death valley and Yosemite are stunning and you won't see the likes of them over here.
If you can spare the time you won't regret it and although some parts are mountainous and windy the roads are in very good condition and easy enough to drive. To be honest I found them far more relaxing and comfortable than the hustle and bustle of the Interstates.

The one thing you must check before leaving is that the Tioga pass is open that crosses the Sierra's at Lee vining[HWY 120] If not, it will have to be the Southern route.