Most of them (?) let you trade without verifying identity, as long as you only withdraw cryptocurrencies. The largest one in Europe seems to be Kraken. Bitfine

Most of them (?) let you trade without verifying identity, as long as you only withdraw cryptocurrencies. The largest one in Europe seems to be Kraken. Bitfinex was one of the first to let people use leverage, but nowadays you can get it on most of them. If you want to withdraw fiat, you'll need to have a verified account (think sending them a photo of your ID/passport and some invoices to verify your location).