* Housing prices leap as tourist numbers surge
* "Like Disneyland" in downtown Reykjavik - Pirate leader
* Tourism lifts economy from 2008 banking collapse
* Tourism, house shortages to figure in Oct. 29 vote
By Stine Jacobsen
REYKJAVIK, Oct 10 (Reuters) - Hunting in vain for a home to rent in Reykjavik, Vally Einarsdottir says landlords either demand too much money or expect her to move out in the summer to make way for tourists who are stoking Iceland's economic recovery.
For many Icelanders like Einarsdottir, a single mother, rising house prices are among the downsides of the volcanic island's tourism boom that has helped the economy back from the brink after a 2008 banking collapse.
Housing shortages and high prices, partly stoked by tourists wanting to see everything from the Northern Lights to landscapes used in the HBO TV series "Game of Thrones", are among the campaign issues ahead of a parliamentary election on Oct. 29.
"The consequence is anxiety. Anxiety over everything. Just looking at the fact that we may be homeless," said Einarsdottir, a 33-year-old who works in customer support at an IT firm. She has been looking for an apartment for herself and her 10-year-old daughter since May.
Speaking in Reykjavik, where cranes dot the skyline, she said she has to vacate her current rental by November as it is being sold. Construction is picking up after the financial crisis, fuelled by demand for homes and hotels.
Einarsdottir said rentals start at around 200,000 Icelandic crowns ($1,760) a month, against the 140,000 she is now paying.
Many landlords prefer to rent to tourists in the summer rather than to Icelanders. That reduces accommodation on the market, inflates prices and imposes conditions such as a requirement to vacate the property from May to September.
Opposition parties say the centre-right government has thrown open the doors to foreign tourists with too little regulation of a huge influx that they say threatens the character of the island.
"It's like the city (Reykjavik) is not my city anymore, it's like Disneyland downtown," said Birgitta Jonsdottir, leader of the anti-establishment Pirate Party, which could form the next government after the parliamentary vote.
Opinion polls show support for the party running at over 20 percent, slightly ahead of the Independence Party, which shares power with the Progressive Party, and is polling at around 12 percent, well below the 24 percent it got in the 2013 election.
Jonsdottir said her party also wants restrictions on the numbers of tourists visiting natural sites outside the city, which often lack of basic facilities such as toilets.
"I as an Icelander used to go there all the time, but I can't go there anymore, it's just too crowded," she said. The party would work to introduce a tax on hotels to make it possible to invest in sanitation and other infrastructure.
Fuelled by the tourism boom, economic growth this year is expected to hit 4.3 percent and the latest data shows a seasonally adjusted unemployment rate of 3.1 percent. Tourism now accounts for more than 10 percent of jobs, according to Islandsbanki.
Icelandic bank Arion estimates that 8-10,000 extra houses will be needed before 2020, in a country of 330,000 inhabitants as demand picks up after the financial crisis. It reckons tourism could make up almost 10 percent of GDP in 2016.
Residential housing prices were up 12.4 percent in August compared with a year ago, according to Arion, while Reykjavik rental prices rose 9 percent in August year-on-year and were up 55 percent from early 2011, data from Registers Iceland showed.
"A lot of the homes that would normally have gone into the market have been bought or used to rent out to tourists," Housing Minister Eyglo Hardardottir told Reuters.
"Tourism is a major change, because of the changes in the way people travel. They travel much more independently," she said. "What I've been emphasising is ... that we get the number of homes up."
Contrasting with the Pirates, Hardardottir's centre-right Progressive Party's campaign points to its success in rescuing the economy and highlights the need for continued stability.
"During this term we've been emphasising lower debt and higher salaries ... The big question for the next term will be with regards to the welfare system like healthcare and education".
The pressure on the housing market is expected to increase as the number of tourists is projected to grow by 35 percent next year against this year to 2.37 million, outnumbering inhabitants by seven to one, Islandsbanki research showed.
The number of properties listed on Airbnb, an online rental portal, jumped 126 percent to around 2,700 by end-November 2015 compared with December 2014, according to Islandbanki.
Last year parliament approved legislation that limits how many days per year people can rent out without a licence. It also imposed an income limit of 1 million Icelandic crowns.
Tourism's rise makes the country sensitive to a sudden slowdown even though the risks are far smaller than with the massive over-dependence on the banking sector that triggered a near-collapse of the economy.
"Should banks become overly concentrated in the industry, a sudden slowdown in tourist inflows could have repercussions on the still-recovering banking sector," Moody's said in a research note, saying loans to the tourist industry constitute around 10 percent of the loan portfolios of Iceland's commercial banks.
A slowdown in the tourists' home countries could also hit demand. The number of British tourists has slowed amid the pound's depreciation after the Brexit vote, said Islandsbanki.
However, the tourism boom is good for the economy overall.
In August, Iceland took a big step in dismantling its 8-year old capital controls and the smooth progress so far has earned the country a double-notch credit rating upgrade and has been driving up its currency. ($1 = 113.5500 Icelandic Crowns) (Additional reporting by Ragnhildur Sigurdadottir, editing by Alister Doyle and Alison Williams)