Nationwide sees a similar picture, predicting a 2% rise over 2017.
"Like most forecasters, including the Bank of England, we expect the UK economy to slow modestly next year, which is likely to result in less robust labour market conditions and modestly slower house price growth," says the company's chief economist, Robert Gardner.
"But we continue to think a small gain (around two per cent) is more likely than a decline over 2017 as a whole, since low interest rates are expected to help underpin demand while a shortage of homes on the market will continue to provide support for house prices."
Savills, though, is more pessimistic, saying it expects prices to remain completely flat through 2017, and rise by just 2% in 2018.
"The effect of Brexit is complicating a natural shift towards the later stages of the housing market cycle, when the strongest growth is seen beyond London and the South East," says Lucian Cook, Savills UK head of residential research.
"What is clear is that the housing market does not like political and economic uncertainty and this points to a lower growth, lower transaction market across the board."
All agree that low interest rates are protecting homeowners from a fall in the value of their property. However, with people under more financial pressure than they have been for years, few will be in a position to take on more borrowing - so there's no chance of a property boom.
This, of course, is good news for first-time buyers. However, Savills believes that these people will be finding it even harder to raise a deposit, and says sales are expected to fall 15% from 325,000 this year to 275,000 in 2018.
And, says the firm, "Tougher lending criteria will also constrain mortgaged home owners looking to trade up."
UK's most expensive houses
UK's most expensive houses
The most expensive property on the open market in London right now isn't even a house. But this five-bedroom apartment has the prestigious One Hyde Park address, with magnificent views of both Knightsbridge and Hyde Park. Like a country house, it's split into two wings, connected by a 50-metre hallway. And the Candy & Candy decor is dramatic, to say the least. It's priced at an eye-watering £64,999,950, through Savills.
This seven-bedroom house has both indoor and outdoor swimming pools, along with a spectacular double-volume entrance hall, panelled study and grand double reception room. There are also two large dining rooms, a cinema room and a staff flat on the lower ground floor. It costs £46,500,000 through Knight Frank.
This 18th-century house has its own spa tucked away in the basement, with swimming pool, gymnasium, steam room, sauna and beauty treatment suite. The "magnificent ambassadorial mansion" has six receptions, eight bedrooms and a separate mews house. It costs £39,500,000 through Savills.
This house may look in pretty good condition to you and me, but the agents reckon it "does require updating to meet today's standards". Built in 2001, Oaklands Park has over 100 acres of land with four cottages, 33 stables and a polo pitch. There are five reception rooms and six main bedroom suites. It's for sale through Savills for £25,000,000.
Just three miles from the middle of Edinburgh, sixteenth-century Craigcrook Castle is up for sale for the first time in nearly three hundred years. It needs a fair bit of work - and a great deal more money - but has gallons of potential. It's up for sale through Ballantynes with a guide price of £6,000,000.
The most expensive property we could find in Northern Ireland right now, Dundarave is a grand mid-eighteenth-century house standing in 595 acres. The extraordinary Great Hall, which rises to the full height of the building, was based on the hall of London's Reform Club. It's on the market for £5,000,000 with Savills.
It may be a little outside the usual footballer's territory, but Swettenham Hall has room for a good kickabout in several of its half-dozen reception rooms. There's an indoor swimming pool and gym, a historic chapel - and a helicopter hangar. It's up for sale with Jackson-Stops for £12,750,000.
This bastion of bling near Exeter was built four years ago and comes with an extraordinary range of features - from equestrian facilities to a helipad and hangar. There's an indoor swimming pool, an enormous garage that's more immaculate than most kitchens, and even an indoor shooting range - as well as a cinema, bar and entertainment suite. It'll set you back £7,000,000 through agents Knight Frank.
"Steeped in history and glamour", say the agents, this Georgian country pile has nine reception rooms and 13 bedrooms. Designed by by Sir John Soane, it features a sweeping double staircase and stunning original features. There's a rumour that Johnny Depp's interested, though, so you may need to move fast to snap it up. It's priced at £5,750,000 through agent Sowerbys.
Near Droitwich, this "faux-Regency house" has nine bedroom suites and four receptions - plus a huge conservatory and an orangery. It has a well-kitted out leisure wing, with pool, gym, sauna, steam room and solarium. Set in parkland, it's approached by an impressive drive. You can snap it up for £9,500,000 through agents Andrew Grant.