I had a look at using one ticket to do all this, and the cheapest option I have found is a Salisbury - Chesterfield ticket, which would allow you to do Salisbury - London - Cambridge - Peterborough - Leicester (change from outward to return) - Birmingham -Bristol or Reading - Salisbury, but because the outward of a (Super) Off-Peak Return expires at 0429 on the third day, you would need an Anytime Return to do this, which is very expensive. You can also do it with a Super Off-Peak Return, with an additional single Cambridge - Leicester, but that will cost altogether almost £90 with your Railcard.
I am unable to beat the suggestion by Hadders on price.