After Piper Alpha's destruction in 1988, the UKCS Oil Industry started looking very carefully at safety issues on Platforms. At the time, the oil price was hovering at or below the average of 20.94 USD / Bbbl. Immediately after Piper Alpha, production was not so important as the massive safety concerns and retrofitting of equipment and proceedures.

Around this time, Brent and others started to go into decline. A drilling campaign was instituted on Brent and a lot of other platforms in order to try and bring production up: Horizontal drilling, 'Kebab' drilling (into slump structures and isolated traps hitherto not easy to reach). The technology was available, the price was right.
Hence the two peaks and a new lease of life. Short of very major discoveries, the second peak will be the last.
 

Thanks for clarifying this.

So if I understand well, it was just unfortunate that Piper accident coincided (more or less) with Brent's decline. That is what exacerbated the drop after the first peak.