You can add "Web n Walk" on T-mobile for a price, an add-on to give unlimited internet access. If you do not have web n walk, internet access is charged according to how much data you download, to a maximum of £1 per day. Web n walk previously cost £7.50 per month, and I think it still costs that for existing customers. As for new customers, I believe they have dropped the price to £4.50 for a "web n walk lite" which is capped, or the £7.50 if you want to get videos and live streaming.
T-mobile currently bar streaming from BBC iPlayer for some odd reason, even though there are multitudes of places where can stream broadcasts from, including France 24 which gives excellent news coverage in English as a good quality alternative to Sky News. It seems T-Mobile bar iPlayer because the company has an agreement with Sky - you can subscribe to Sky Sports or Sky Movies on T-Mobile if your phone supports video streaming, and you have unlimited internet (£5/month for Sky).