Depends on what you mean minimum cost. Orange do a contract for £35 with unlimited anytime texts and 600 call minutes.
Or £25 no minutes and 3000 texts.
On their PAYG, stick a minimum of £10 in a month and you get 300 free any time texts.
Three are doing a contract for £15 for life, 75 call minutes and 600 texts and a free Nokia 6280r, offer ends 31/03/07.