The question facing all users: What to do with the waste?
As always: reprocess, partition, re-use, and wait.
- Left-over uranium -- hundreds of tonnes per reactor-year. Uranium is stable and harmless if it's kept as the oxide (or, surprisingly, if it's dissolved in the sea, because there's so much there already, it won't make a difference.) It can be used to breed fuel, though, so worth hanging on to.
- Plutonium bred in the reactor -- less than one tonne per reactor-year. Keep it, and save mining uranium by consuming it as fuel in future reactors. Don't be spooked by the name: Plutonium for bombs has to be specially made. A rational terrorist wanting nuclear explosive would use natural uranium and enrich it, as the Iranians are said to be doing.
- Short lived fission products -- hundreds of kilos per reactor year. Handle with great care, for a while, and with caution for longer. These materials are dangerous to be close to for many years and must be kept out of the biosphere for hundreds (but not thousands) of years.
- Long lived fission products -- kilos per reactor year. Obviously much less radioactive than the short-lived products, the rational thing is simply to abandon in the deep ocean. But it appears possible to transmute these products to short lived waste with neutron irradiation, and that would be a more "grown-up" approach!
The point about nuclear waste is the quantities: once the re-useable components are removed, the volumes are million-fold reduced over combustion energy. A year's fission-product waste from a reactor, once it had cooled off for thirty years or so, could sit on a few dozen yards of industrial shelving. A facility to retain the waste of a largely nuclear Britain for the necessary 500 years or so would take up less space than an industrial estate.
The idea of nuclear waste as being dangerous for tens of thousands of years is an Americanism, arising from their reluctance to reprocess. If you leave it all mixed up in the fuel rod, then yes, it is hard to manage. But if you make the sensible choices, then the problem -- looked at on the scale appropriate to global energy generation -- goes away.