Nationally, annual house price growth accelerated to 13.4% in June, marking the strongest growth since November 2004, according to the index.
Across the UK, the average house price in June was £245,432, Nationwide Building Society said.
Prices were up by 0.7% month-on-month, following a 1.7% increase in May.
Robert Gardner, Nationwide’s chief economist, said: “Prices in June were almost 5% higher than in March.”
Mr Gardner said that while mortgage rates remain close to all-time lows: “House prices are close to a record high relative to average incomes.
“This is important because it makes it even harder for prospective first-time buyers to raise a deposit.
“For example, a 10% deposit is over 50% of a typical first-time buyer’s income.
“A potential buyer earning the average wage and saving 15% of take-home pay would now take five years to raise a 10% deposit.”
A stamp duty holiday will be tapered from July, before reverting to normal levels this autumn.
Mr Gardner said: “Activity will almost inevitably soften for a period after the stamp duty holiday expires at the end of September, given the strong incentive for people to bring forward their purchases to avoid the additional tax.”
He added: “Underlying demand is likely to soften around the turn of the year if unemployment rises as most analysts expect, as Government support schemes wind down.
“But even this is far from assured. Even if the labour market does weaken, there is also scope for shifts in housing preferences as a result of the pandemic to continue to support activity for some time yet.”
The report also looked at house price changes across UK nations and regions in the second quarter of this year, compared with the same period a year earlier.
Mr Gardner said: “Northern Ireland was the strongest performing region, with prices up 14% year-on-year, the highest rate of growth since 2007.
“Wales also saw a significant acceleration in annual house price growth to 13.4%, the largest rise since 2005.
“But conditions were more muted in Scotland, which saw a modest increase in annual growth to 7.1% (from 6.9% last quarter) and was also the weakest performing part of the UK. This may reflect (the fact) that the (equivalent property tax) holiday in Scotland ended on March 31.”
Here are average house prices in the second quarter of this year and the annual growth, according to Nationwide Building Society:
– Northern Ireland, £163,576, 14.0%
– Wales, £183,728, 13.4%
– Yorkshire and the Humber, £183,982, 13.0%
– East Midlands, £210,753, 12.2%
– West Midlands, £218,334, 12.2%
– North East, £144,014, 11.2%
– Outer South East (includes Ashford, Bedford, Braintree, Brighton and Hove, Canterbury, Chichester, Colchester, Dover, Eastbourne, Hastings, Lewes, Rother, Wealden, Fareham, Folkestone and Hythe, Gosport, Havant, Isle of Wight, Maldon, Milton Keynes, New Forest, Oxford, Portsmouth, Southampton, Swale, Tendring, Test Valley, Thanet, Uttlesford, Winchester, Worthing), £313,815, 10.9%
– North West, £188,730, 10.9%
– South West, £277,603, 10.4%
– East Anglia, £253,107, 9.7%
– Outer Metropolitan (includes Basildon, Bracknell Forest, Brentwood, Chelmsford, Crawley, Dartford, Epping Forest, Gravesham, Harlow, St Albans, Stevenage, Watford, Horsham, Luton, Maidstone, Reading, Rochford, Rushmoor, Sevenoaks, Slough, Southend-on-Sea, Elmbridge, Guildford, Runnymede, Spelthorne, Tandridge, Waverley, Woking, Thurrock, Tunbridge Wells, Windsor and Maidenhead, Wokingham), £394,295, 8.2%
– London, £509,935, 7.3%
– Scotland, £165,745, 7.1%