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 $r{A}$, 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 $r{A}$ 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 $r{A}$ lag those at 1315 $r{A}$ by $0.29pm0.06$ day, while the fast variations are coincident ($0.04pm0.12$ day). The UV/optical continuum reverberation lag from ${it IUE}$, ${it Swift}$ and other optical telescopes at different wavelengths are consistent with the relationship: $tau propto lambda^{4/3}$, 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.
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