Do contactless cards work through a wallet?*
Oh yes. Not only through a wallet but also through a couple of layers of clothing in addition!
When I’d reach the Tube Station, I’d have a laptop bag on one shoulder and a shopping bag on the other. On top of that, during winter, I’d have a jacket and an overcoat on top. Amidst all those encumberances, it would be a major PITA to take out my Oyster Card from my wallet. So, I wouldn’t.
As I reached the turnstile, I’d just nudge the pocket where my Oyster Card-bearing wallet was located towards the card reader. Nine out of 10 times, it did the trick and the turnstile would open without my having to take the “concealed” card out of the wallet.
For the uninitiated, Oyster Card is a contactless stored value transit card for use on Tube, Bus, DLR, Ferry, and other Transport for London modes of transport.
Now, if “contactless cards” in your question really meant “contactless payment cards”, my answer would be no different from the above although I must admit that I’ve never tried to pay with a “concealed” contactless credit card at a POS.
In fact, ever since PINless regime was enforced in my jurisdiction, I have removed my contactless debit cards from my wallet. I now keep them at home and take them out only when I go to the ATM to withdraw cash.
I’ve read about “RFID Wallet”, which supposedly shields concealed contactless cards from getting accidentally “tapped” at a POS or by a fraudster armed with a card reader in your vicinity. But I haven’t tried one yet.
*: This is the original question I answered. I’m repeating it to help me make sense of my answer in case it’s moved to / merged with some other question that I didn’t answer.