three do a deal for £10 a month with 3000 texts, 75 mins talk time and a gig of data. that is sim only... ask at the carphone warehouse - am in the market for a contract atm and that was what they recommended me.
My DD & OH use the £10 a month option (called goody bags) which gives them unlimited texts, truly unlimited Internet and 250 UK mins.
This month I've tried DD on the £5 a month which still gives unlimited Internet but only 60 mins & 300 texts. Point is that its flexible and they use the O2 network too, as well as being owned by O2.
The only small fly in the ointment is they don't send out microsim's directly but if you are interested, PM me and I can sort you one out. The really cool thing is that if you sign up as a result of my "referral", we both get £5 credit added to our accounts. Win-Win.
Honestly it's the best network I've used and given you say you don't text/talk much and only need the Internet, I think the £5 labs option would give you a good taster. If you don't like it you are not tied to a contract.