If your relative lived and and had their death registered in the same registration district, that may narrow down the number of possible cemeteries/crematoria you would need to approach to locate a final resting place.
www.yell.com should help you in this regard.
With many years experience of the funeral trade, I would not hold out too much hope that they still have the records you seek from 1989/1990. If records survive, they will only contain information about the particulars of the funeral - date and place, fees etc, but if you have contacted the cemeteries/crematoria you might already have located the correct place and be succesful in that regard.