Thanks to Gerry Wolff for this extremely valuable resource.

There is no question that renewables can meet the UK's present and anticipated future demands for electricity, even allowing for future uses of electricity for such things as space heating (eg using electrically-driven heat pumps) and the electrification of transport by road and rail -- more below. Here is some of the evidence:

A network of land-based 2.5-megawatt (MW) turbines restricted to nonforested, ice-free, nonurban areas operating at as little as 20% of their rated capacity could supply more than 40 times current worldwide consumption of electricity and more than 5 times total global use of energy in all forms. There is additional potential in offshore wind farms. See Global potential for wind-generated electricity (PDF, 1.9 MB, Xi Lua, Michael B. McElroya, and Juha Kiviluomac, Proceedings of the National Academy of Sciences of the United States of America, June 22, 2009, doi: 10.1073/pnas.0904101106, http://www.pnas.org/content/early/2009/06/19/0904101106.full.pdf+html).
The "economically competitive potential" of wind power in Europe comfortably exceeds projected demands. In principle, it could meet all of Europe's energy needs as well. See Europe's onshore and offshore wind energy potential (PDF, 3.5 MB, European Environment Agency, 2009, http://www.mng.org.uk/gh/resources/Europes_onshore_and_offshore_wind_energy_potential.pdf).
Wind, water and solar technologies can provide 100 percent of the world’s energy. See "A path to sustainable energy by 2030", an article by Mark Z. Jacobson and Mark A. Delucchi in the November 2009 issue of Scientific American, and Review of solutions to global warming, air pollution, and energy security (Mark Z. Jacobson, Energy & Environmental Science, 2009, 2, 148–173). See also the interactive presentation about this research: Powering a green planet: sustainable energy, made interactive (Scientific American, November 2009). In the scenario described in the Scientific American article, wind supplies 51 percent of the demand worldwide, provided by 3.8 million large wind turbines (each rated at five megawatts). Although that quantity may sound enormous, it is interesting to note that the world manufactures 73 million cars and light trucks every year.
The variability of sources such as wind power is much less of an issue than is sometimes suggested, as described in Managing Variability (PDF, 402 KB, Greenpeace, WWF, RSPB, Friends of the Earth, July 2009, http://www.trec-uk.org.uk/reports/milborrow_managing_variability_final_July_2009.pdf). Fluctuations in wind strength can be managed technically and at modest and declining cost, high proportions of wind power are feasible in the UK's energy mix, and new technological developments could allow for a steadily increasing use of wind power and the phasing out of conventional carbon based fuels as a backup technology. See also "Matching variable electricity supplies with variable demands", http://www.trec-uk.org.uk/elec_eng/supply_demand.html.
Photovoltaics could generate about 266 TWh in the UK - about 66% of the UK's present electricity demand. See Renewable Energy and Combined Heat and Power Resources in the UK", Tyndall Centre, 2002, http://www.tyndall.ac.uk/sites/default/files/wp22.pdf)
Using concentrating solar power (CSP), less than 1% of the world's deserts could produce as much electricity as the world is using. Less than 5% of the world's deserts could produce electricity equivalent to the world's total energy demand. These calculations, which are quite conservative, are based on research from the German Aerospace Centre (DLR). Although it would be possible to obtain all the world's energy from deserts, there are several reasons why Europe and the UK (and other regions and countries) should use a variety of renewable sources of power, as described in the TRANS-CSP report from the DLR which may be downloaded via links from http://www.trec-uk.org.uk/reports.htm.
The government's own plans for the growth in renewables and energy conservation in the UK can ensure adequate generating capacity in the UK until at least the mid 2020s. See Implications of the UK meeting its 2020 renewable energy target (PDF, 734 KB, Pöyry Energy (Oxford) Ltd for WWF-UK and Greenpeace-UK, August 2008, http://www.mng.org.uk/gh/resources/Implications_of_UK_renewable_energy_targetv1.0.pdf).
There are now several reports on how to decarbonise the world's economies via renewables and the conservation of energy. Many of them are listed, with notes and download links, on http://www.mng.org.uk/gh/scenarios.htm.

Future developments

Electrification of road and rail transport in the UK would add to the UK's demand for electricity but not as much as one might think:

In terms of energy, about 50% more electricity would be needed (see Appendix 8 of "Energy UK" (PDF, 378 KB, http://www.mng.org.uk/gh/resources/energy_UK3.pdf). The reason it is not more is that electric motors are very much more efficient than internal combustion engines. Much of the energy that we are using now for overland transport is simply wasted.
In practice, the additional amount of generating capacity that will be required is likely to be less than 50%. This is for two reasons:

It is likely that much of the charging of electric vehicles will be done at night when there is likely to be a lot of spare capacity from sources such as wind power. To that extent, it does not add to the generating capacity that would be required.
The electrification of road transport will facilitate the introduction of grid-to-vehicle technologies allowing two-way flows of electricity between vehicles that are on charge and the transmission grid. This will help to keep demands for electricity in balance with supplies, thus helping to minimise the amount of spare capacity that is required.

It seems likely that, in the future, there will be increasing use of electrically-driven heat pumps to provide space heating in buildings. But, with good insulation of buildings and the use of technologies such as inter-seasonal heat transfer (see, for example, http://www.howedell.herts.sch.uk/eco_issues/sustainable_elements.pdf), residual needs for the heating of buildings could turn out to be small.

Energy costs

Accurate information is critically important in any kind of cost-benefit analysis. In weighing up the pros and cons of various sources of power, it is important to take account of the fact that energy markets are distorted:

In a report published in 2004 (http://news.bbc.co.uk/1/hi/sci/tech/3818995.stm) the New Economics Foundation made a conservative estimate that worldwide subsidies for fossil fuels amounted to about $235bn a year—and there seems not to have been much change since then.
The continued existence of subsidies for oil, gas and coal is confirmed by recent reports that the G20 countries intend to remove them (see, for example, http://www.reuters.com/article/environmentNews/idUSTRE58O3RN20090925).
Contrary to what is suggested by the nuclear industry, and widely believed, nuclear power is heavily subsidised. The subsidies are described in Nuclear Subsidies (PDF, 167 KB, http://www.mng.org.uk/nsubsidies.pdf), a report from the Energy Fair group. If just one of those subsidies was to be removed—limitations on liabilities—the cost of nuclear power would rise to about 41 US cents per kWh, a level that would make it deeply unattractive to investors.
There is still no global cap on emissions of CO₂ and schemes such as the EU ETS are not working properly. For those kinds of reasons, the price of CO₂ emissions is far too low.

Removal of these distortions would transform our perception of what is or is not 'economic'. It is likely that most renewable sources of electricity would be seen to be cheaper than electricity from fossil fuels or nuclear power.

Removal of these distortions would mean that subsidies for some renewable sources of power could be reduced or removed altogether (see http://www.nonukes.org.uk/reducing-subsidies).

There would probably be a need to retain subsidies for renewables that have not yet reached the bottom of their cost-reduction curves.

In some cases there may be special reasons for providing support. For example, if the majority of people feel that onshore wind farms spoil the landscape (and that is by no means clear) there may be a case for providing a subsidy to cover the extra cost of putting wind turbines out at sea.