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First London to Edinburgh is not a mini tour, if you want to cycle back as well - it definitely is not a mini. So at 85 miles per day thats 4 days each way!
There are other touring threads which might be better places to post about your planned tour. Do you already have a rack and panniers? If so just use those. If your bike can't take a rack then look at the frame bag and saddle bag combo by all means. I want an Apidura saddle bag myself, but I am intending to use it on my trails bike, where being lighter make more of a difference and I am not away for more than a few days. (Probably some 300km+ Audax rides too, once I grow a pair and commit to doing one.)
Panniers are hard to beat when you need to carry a decent load over a bigger period of time!
Am considering a first mini tour from london to edinburgh and back (with a few days recovering in Edinburgh), using the LEL audax route. Staying in BnBs along the way. Looks like around 85 miles a day. Only have a road bike and want to go as light as poss so thought I'd try an apidura saddle bag plus maybe a frame bag or handlebar bag to distribute weight. What do people think?