My understanding is that, in the UK, a purse is a wallet/coin purse. The larger sack you stick the wallet/coin purse into, what we'd call a purse, is a handbag or a shoulder bag (depending on strap length).
Men still carry wallets, though I don't know if a (natively BritE speaking) woman who keeps her (UK) purse in her pocket, not her shoulder bag, might refer to it as a wallet.