score:11
No there isn't.
Or at least in the forty years since I started driving in Britain I have never heard of one. One of the reasons is that the number of letters that will fit in the road varies, so for every town there might be several abbreviations of different lengths.
The good news is that these abbreviations are almost never used on street signs, only on road lanes. This means that the worst that can happen if you get one wrong is that you end up in the wrong lane, not going the wrong way. (If you aren't able to change lanes fast enough you might end up going the wrong way briefly, but you usually realize and can go back around and be in the right lane).
These abbreviations are used to indicate a general direction. So you should be aware that 'Reading' is in the direction you want to go. You can be pretty confident that it doesn't mean another town beginning with R, even if you don't get the abbreviation exactly.