I would say that given your budget you are going to be limited to a consumer lens and one of the best of the bunch is the 18-70 (definate improvement on the 18-135 - I should know). You also have the option of the Sigma 24-70 f2.8 which would compliment the 10-20 nicely and is an f2.8 throughout.
Though I struggle to understand why you are upgrading to a D300 (~£1000) rather than spending that money on some pro quality lenses e.g. the 17-55mm (or perhaps the stunning Nikon 24-70 f2.8 which is also full frame compatible) and sticking with your D80 for a little bit longer. If you want a Semi-Pro spec SLR then you may be able to find a D200 for about £400 (just a little over your lens budget).
Just my 2p worth.
however i have read that the D300 improves lens quality and auto speed among other advantages which rises above the D80 & D200,
That seems right and has been documented several times. I have the Nikkor 70-300VR, I dont think you will go wrong with that one. I also have an 18-200VR and although it was always good ( on D50 D70s D80 and D200) on the D300 it is so much better and feels a totally different lens. Your 10-20 Sigma should be great on a D300 too.
How about taking your 18-135 into Jessops and asking to put it on a D300 body. Take a few shots on your own card (CF) and have a look at them at your leisure, see if you still get a quality issue, but honestly, you dont need the 135 if you have the 70-300.
I would get the D300, keep your two lenses and spend the £250 on a mid range zoom, plenty of suggestions above.
Allan