I just bought a £45 phone...
...and it ain't bad at all! Seriously, it hasn't annoyed me once yet!
I needed a phone that day (having punched my painfully slow £25 (unlocked, from Sainsbury's) Alcatel Pixi 3 in the screen for refusing to read an SD card properly the day before) and went to an EE shop. I didn't want to spend much because I have a fancy phone in need of expensive repair. The price tag said £90 for a Huawei Y560, but the manager had a ring-binder and said I could have it for £45.
I'm really happy with it. Within 5 minutes of opening the box - it shipped with the battery at 50% charge - I'd popped in my EE contract SIM, restored my contacts from Google and had a fully functional phone. It's snappy and doesn't pause or lag for normal tasks (the Snapdragon 210 gets warm during modest strategy games, no matter), it's 4G, Android Lollipop, has a camera flash, GPS, 1GB RAM... I really can't find any major shortcomings with it. SD card slot, replaceable battery, it's all there. At its list price it has some competition, but at £45 it is amazingly good value.
If you do buy a budget phone, the important thing isn't the internal storage (most have SD card slots) but the RAM - shockingly, some Android phones are still sold with less than 1GB of RAM which is just asking for frustration.
(Meanwhile, the quoted repair cost for my Sony Z3 Compact remains £85. It's like when my mate's Hitachi disc cutter died and rather than pay £80 to fix it he bought one from Lidl or £50 with a 3-year guarantee)