enamay - these are just my thoughts.
It is likely that with no family she was cremated rather than buried (sad to say the cheaper option)
If this was the case the closest crematorium is Worthing Crem. which is in Findon. This had opened in 1968 so was a new facility.
Perhaps her ashes were then scattered in the garden of remembrance there, it's unlikely they'd have paid for an interment in a churchyard elsewhere if she was cremated.
Perhaps contact the crem.
http://www.worthingcrem.co.uk/ as your first step

Other records could be with the West Sussex Record Office in Chichester but as this was 1969 they are likely to be closed so you won't be able to access them.
Others may have other thoughts...
suey