This is something I myself had to sort out recently.
Apparently there are now 5 Exam Boards in the UK excl Scotland. That is 3 in England, 1 in Wales, 1 in N Ireland. City & Guilds is in London. The old boards with whom you did your exams will have merged into one of the above now.
To get copies of your certificates you need to contact the exam boards in turn to find out which has the old records for the old exam boards you did your exams (why not ring your old school and ask them which Exam Board) with and send them a fee together with evidence that you are who you say you are, so as to avoid identity theft of course.
If all you need are the results, then ring the school - thty might even have yoyr certificates if you hadn't collected them, though they should be able to help you with the Exam board.
Depending upon your age, and the fact you have O levels as opposed to GCSEs tells me you are of a certain age, you need to decide whether it is worth your while to have certified copies.
As an example, I did O Levels in 1969 and 1970 and A Levels in 1972 all with one Exam Board, the WJEC, in Wales. They expected me to send them 20 Uk pds for the first certificate with a max of 30 Uk pds for the rest. I am yet to do sort it out but I am sure all the boards will be very helpful.
This explains the legality issues at least for the WJEC:
Your starting point for these Exam Boards is here:
Good luck in your quest and i hope you will find the process as easy as I did. If you found this info helpful, please consider leaving some positive feedback for me. JA has very few UK Experts and I try hard in the areas of my own expertise to help the Brit contingent.