We're not talking about a plant being down for a few hours, it'd be a few months for the existing plant to be decommissioned and the new plant to be installed, assuming the existing footprint does not allow the two plants to exist side by side
But yes, many existing nuclear sites may be an ideal location if available.
The grid is designed to deal with the loss of a power station like this. In fact it does all the time as generators go offline for maintenance etc.
Also, the land requirements for this are really modest. Our legacy power station sites are pretty big. The old coal stations needed a lot of space for coal. The nuclear sites tend to be built in rural areas surrounded by countryside. There are also quite a few that were built on massive WWII airfields and have huge areas. Finding land will not be a problem.
My guess is that the biggest issue will be finding a site with suitable geology (for the hole) and access for heavy/wide vehicles.
But yes, many existing nuclear sites may be an ideal location if available.