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That's Greek to me
get an electrician in
if you're not confident/prepared to try and isolate the fault, then if you have two new replacement sockets you're going to have to replace anyway..
..or else live with unreliable sockets - worst case is that the back box is screwed to combustible material, there's a slow earth fault and earth leakage current (the back box in the picture is not earthed..) meets high resistance, snowballs (logarithmic heat accumulation), resulting in fire.
That's Greek to me. I just undid all sockets, tightened up connectors (some were loose) and tried them all: same as before. Left-most one works fine, next to the right one works and the other is intermittent, right-most socket both are intermittent. I can't quite bring myself to actually undo all the connectors and put the new sockets on to the two that are playing up to see if that fixes it.