I am sorry to have to tell you that there is no 1868 aluminium proof set in the Bank of England. Briefly, the history of the Bank’s coin collection is as follows: its original collection of coins , begun in 1811, was given to the British Museum in 1865 to allow greater public access. The present collection was begun in 1932 with the aim of compiling a representative collection of British regal coins issued since 1694, the year the Bank of England’s foundation. A large number of old coins were held in the Cashier’s Department and further coins bought from dealers to fill gaps. Apart from a few rarities the collection was completed by 1950 at an approximate cost of £830! Further additions have been made since then, and continue to be made.

I’ve had a quick look through the collection and cannot find anything. The transfer of objects from the Bank of England took place in 1865, predating the production of these coins by three years. I think it’s unlikely that they ever came to the British Museum.