Is there a way I can find my biological father? His name's not on my birth certificate.?

My mum had an affair and I was brought up thinking another man was my father. I only found out last year (aged 22) that he wasn't. The only information I have is his name, his surname's unusual and I don't know how to spell it, and his location back in 1984. Have tried loads of different spellings & he doesn't seem to be on electoral register/friends reunited/genes reunited etc. Can't afford a private detective & don't know where to turn. Most charities only help adoptees and I'm the result of an illicit affair. Feel crap and would appreciate any advice. Thanks.