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Using a month-long X-ray lightcurve from ${\it RXTE}$/PCA and 1.5 month long UV continuum lightcurves from ${\it IUE}$ spectra in 1220$-$1970 $Å$, we performed a detailed time-lag study of the Seyfert 1 galaxy NGC 7469. Our cross-correlation analysis confirms previous results showing that the X-rays are delayed relative to the UV continuum at 1315 $Å$ by 3.49 $\pm$ 0.22 days which is possibly caused by either propagating fluctuation or variable comptonisation. However, if variations slower than 5 days are removed from the X-ray lightcurve, the UV variations then lag behind the X-rays variations by 0.37$\pm$0.14 day, consistent with reprocessing of the X-rays by a surrounding accretion disc. A very similar reverberation delay is observed between ${\it Swift}$/XRT X-ray and ${\it Swift}$/UVOT UVW2, U lightcurves. Continuum lightcurves extracted from the ${\it Swift}$/GRISM spectra show delays with respect to X-rays consistent with reverberation. Separating the UV continuum variations faster and slower than 5 days, the slow variations at 1825 $Å$ lag those at 1315 $Å$ by $0.29\pm0.06$ day, while the fast variations are coincident ($0.04\pm0.12$ day). The UV/optical continuum reverberation lag from ${\it IUE}$, ${\it Swift}$ and other optical telescopes at different wavelengths are consistent with the relationship: $τ\propto λ^{4/3}$, predicted for the standard accretion disc theory while the best-fit X-ray delay from ${\it RXTE}$ and ${\it Swift}$/XRT shows a negative X-ray offset of $\sim$0.38 days from the standard disc delay prediction.