Hm.
I'm assuming, if your mother was a pensioner, that you and your cousins are in your 40s or so. Is your aunt still alive? Do you know any details, like a date, sex, name of the institution?
I found out I had a half-sister in my 20s - my mother was pregnant as a teenager before abortion was legal. The thing which screwed me up was the trust - most of my mother's generation knew. What else had they hidden from me? Could any of them be trusted?
I told my full-sister. She had always suspected there was something and had chosen not to know, so she was really angry I'd told her - but if she later found out I knew and hadn't told her, I suspect she'd have been angry about that, too. In contrast, I'd never had the tiniest inkling, so it was a complete shock to me.
There were things I wanted to know for myself, having been told the basics, but I asked my half-sister without my full-sister's involvement. I never dared speak to our mother about it. (We did not have a great relationship.)
So... I guess you will have thought about how they will react if you tell them, and if it's positive, that's great. What will you do if it's not? What if it makes one of them angry and they direct it at you? I think I would see what I could find out before speaking to them. What if you could trace the person, and they don't want to know?
I think they probably ought to know, but once you've told them, there's no going back, whereas if you decide not to, there's the option of changing your mind in future. But whatever you do, tread carefully - it might not be welcome news. I don't think it's possible for them to know without your involvement, though. There's great potential for hurt feelings all round. I don't know what I'd do.