For me the main value of low GI foods is if my insulin system can dispose of the BG fast enough to cope with the food dumping glucose into my system and hence I am able to head off spikes! To this end, I would try the experiment and see if it spikes you excessively or not1
Rye Bread does have a much lower GI than White bread, but it is still Carbohydrate so ultimately will cause your BG to rise, and require an Insulin response.
There are other breads which are lower in carbs such as HiLo which has 5g of carb per slice, you can get it in Sainsbury's. Another one is Lovelife which is also quite low in carbs. You can pick this up in Asda and other supermarkets but as with both these breads they are not widely in demand so not all supermarkets stock them on a regular basis and when they do they usually only hold small stocks. Burgen is quite good too and more readily available.
Sorry my mistake again, it's not LoveLife that's low in carbs, it's Livelife and has only 3.8g of carb per slice. It has less wheat flour as they use vegetable protein flours instead. It has a different taste but is better in my view when toasted. You can get at Waitrose.