The biggest players are Boku casinos and Payforit. Boku is an independent payment provider. Payforit is the payment solution created in cooperation with the major UK mobile carriers.
Even though casinos are using Payforit, they may call it something else, e.g. Pay by Phone, Mobile Pay etc.
The Nordic mobile billing services Zimpler and Siru Mobile are not yet available in the UK. Fonix is slowly making its way to the casino market.