I didn’t have any success at the big-name places like high street banks or the post office, but the first small, one-desk generic no name exchange bureau I went next to Victoria station had no problem giving me exclusively $100s (and gave a reasonable rate).
So I’d suggest simply going to an area with plenty of small / independent exchange shops (there tend to be clusters near the big stations) and ask until you find one with a good rate that is flexible on notes.
It seems like, the smaller and more informal the exchange shop, the more likely they are to dish out cash from simple rolls of bank notes rather than having pre packed bundles or restrictive policies.
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