Best Burner Phone for a Month in London?

This has become somewhat of a perennial AskMe question (previously in 2013, previously in 2012, previously in 2007), but as the mobile communications landscape is ever-shifting, it never hurts to have up to date information. So, if I'm spending the month of August in London, which of the several offerings is the best PAYG-SIM phone to grab upon arrival? I will be bringing my iPhone (AT&T), but turning off data roaming and using it as wi-fi only when I can. Are there deals on low-end smartphones that are worth the extra cash, or is it still best to just grab a simple flip-phone with SMS?