Lost Neutral?

13amp. two double two single sockets the plug in tester shows power and earth lights but no neutral.
Have tested one of the sockets using tester screw driver and the live obviously lights but so does the neutral but not as bright.
Any suggestion before calling electrician to change the Wylex C.U to modern and to test the lost neutral.
I don't want to be stitched up. One electrician many moons ago wanted £800 to change c.u. when average price after son searched internet was £400, but had to put on hold until now, expecting its gone up to say £600, straight forward on wall at eye height no cupboard, cash job half start half when completed.
Grateful thanks to both readers and responders.