This might well be the cheapest smartphone with 1GB of RAM. I speak of the Virgin ZTE Blade Q mini, currently £29.99 at Argos (was £49.99). There’s an obligatory £10 top-up, though you might be able to circumvent that using FastTrack (where available).
ZTE Blade Q Mini specs include a 4in IPS display (480 x 800), 1.3GHz dual-core processor, 1GB of RAM, 5MP rear camera, 4GB expandable storage, Jelly Bean Android 4.2, and a 1,500mAh battery.
Initially locked to Virgin Mobile, but can be unlocked for £1.29 on Google Play thanks to ZTE Blade Q Unlock.
Store collection only; not available for home delivery.
(Thanks to mobjw at HUKD)