Rare ledgers reveal shoe-buying habits of Tolkien and Waugh

does anyone here think that that is JRR's signature? Someone I know is adamant that it is; but I say not.

No it is not, this has come up a couple of times in the past, here is an example, http://sacnoths.blogspot.co.uk/2017/02/tolkiens-cobbler.html, but the answer is quite obvious.

I am a customer of an Oxford shoe shop, I buy an item from them, and then after paying, they ask me to fill in their purchase ledger with details of what I have purchased?

If that was the case, you would not have very happy customers in your shop, so the shop staff fill in the purchase ledger, not the customers.

I would imagine that the only chance of them having Tolkien's signature, is that he had an account with them and had to sign for items on his account, paid by signed cheque, and they kept the cheque instead of taking it to the bank, or sent them a signed letter to order shoes.

The ledgers are not one of the above three chances.

Why was the Professor charged an extra 1 shilling on June 7th 1950, can't work out the writing?

Agreed. The idea that the customer would write his own details in such a ledger is patently absurd.

Cream isnt it !
Personally i use polish