London house prices were up 14.9% last year with the average London home costing £345,186 last year.
Nationwide figures have shown average UK homes prices increased by 8.4% last year.
The study also found that house prices across the UK are at their highest since June 2010 even though prices remain around 5% below all-time highs recorded in late 2007.
Manchester was named the best-performing area for house price rises in 2013, with prices up by 21% and the average home value of £209,627.
Carlisle emerged as the worst performer, with a 1% annual increase in prices pushing the average value of a home to £136,128.
Nationwide said that the rise in house prices can leas to an “affordability crisis”.
Robert Gardner, Nationwide’s chief economist, told the Standard: “The risk is that if demand continues to run ahead of supply in the quarters ahead, affordability may become stretched.
“House price growth has been outstripping average earnings growth since the start of the year.”
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