The four former Laker Airways BAC1-11-300's were purchased by British Caledonian Airways on the 01 April 1982. The four aircraft we're registered to British Caledonian Airways as Musket90 rightly points out.
I'm assuming that all four aircraft we're eventually repainted into the full British Caledonian Airways livery as I can't remember seeing any BAC1-11's at London Gatwick Airport during the summer of 1982 still in the former Laker Airways colour's.
The four former Laker Airways BAC1-11-300's didn't last long with British Caledonian Airways and all four we're eventually sold between September and November 1983.
Here is a photo of the former Laker Airways BAC1-11-300 G-AVBW taken on the 01 April 1982 at Manchester Airport, the day it was re-registered as G-BKAU with the Laker details painted over.
Although I don't have much else to go on but I'm uploading some details of the four former Laker Airways BAC1-11-300's after they were sold by British Caledonian Airways between September and November 1983. As was the case with many former BAC1-11's, they eventually found themselves in Nigeria operated by Okada Air.