* UK real wages suffer biggest fall in G7 since crisis
* Jobless rate at lowest since 1975
* But wages have risen less than inflation
* Employers, unions doubt BoE pay growth forecast for 2018
* Low productivity and insecure work weigh on pay prospects
LONDON, Aug 25 (Reuters) - Britain's economy faces a paradox. Unemployment has fallen to its lowest since 1975 but no end is in sight to the longest squeeze on pay in more than 100 years.
Businesses and trade unions think workers are unlikely to see the 3 percent increase in average earnings that the Bank of England predicts for next year, despite record employment levels and widespread reports of shortages of skilled workers.
Wage growth has been weak in many countries over the past decade, but in Britain the break with what was the norm before the 2008-09 global financial crisis has been particularly acute.
Shifting employment patterns have weakened workers' ability to demand a greater slice of the pie from employers -- and the size of that pie is growing more slowly than before because of a slump in productivity growth.
One top BoE official has even questioned whether Britain is returning to the wage stagnation that dogged the country for centuries before the 18th century Industrial Revolution.
For Larry Joyce, chairman of metal foundry Kimber Mills, keeping a tight grip on wage costs is essential.
Four percent annual pay rises were typical in Britain before the financial crisis. Now Joyce tries to raise wages by no more than the BoE's inflation target of 2 percent. During the worst of the crisis, pay was frozen.
In good years, most staff can expect a bonus from a profit sharing scheme.
"But it's for one year. So if things dip back down again, you are not saddled with a level of wages you can't sustain," he explained.
Weakness in British wages pre-dates last year's vote to leave the European Union but concern about Brexit is among factors that make Joyce doubt wages will rise faster in future.
Most British companies take a similar view. The Chartered Institute for Personnel and Development, a professional body for human resources staff, said 2 percent is the most common annual increase in basic pay in the private sector.
In the public sector, pay rises have been capped at 1 percent since 2013 as part of government austerity measures.
"Employers are not under pressure to raise wages," CIPD labour market analyst Gerwyn Davies said.
The result is that after inflation is taken into account, average pay in Britain last year was 2.7 percent lower than at its peak in 2007, according to figures from the Paris-based Organisation for Economic Co-operation and Development (OECD) think tank.
By contrast, average pay rose nearly 18 percent in real terms between 2000 and 2007.
The 2.7 percent fall puts Britain in bottom place among the world's seven largest advanced economies. In Europe only Greece and Portugal have fared worse.
Britain's shortfall looks set to worsen this year because of the pick-up in inflation since the Brexit vote. Pay grew 2.1 percent in the second quarter, but inflation was up 2.7 percent.
JOBS, BUT NOT AS YOU KNOW IT
What makes Britain different to Greece and Portugal is that, on the surface, its labour market appears to be booming.
Unemployment fell to 4.4 percent in the three months to June, its lowest rate since 1975. Unlike in the United States, where unemployment is similarly low, there are not large numbers of people who have given up looking for a job.
However this masks a big fall in job security for many Britons, and a weaker bargaining position for others.
The number of workers on "zero-hours" contracts, which offer no guaranteed work and in practice often tie them to a single employer, peaked at 905,000 late last year. One million part-time workers also want full-time work.
"Workers do not feel confident enough to ask for a pay rise," said Kate Bell, a senior official at Britain's Trades Union Congress.
Bank of England data show rates of trade union membership are the lowest since the 1930s, while the proportion of British workers who are self-employed is the highest since records began in the mid-19th century.
It was in this context that the BoE's chief economist, Andy Haldane, highlighted similarities between the weak response of wages to falls in unemployment since 2013, and a much longer period of stagnation between 1500 and 1700.
"Prior to the Industrial Revolution ... most workers were self-employed or worked in small businesses. There were no unions. Hours were flexible, depending on what work was needed to collect the crops, milk the cows or put bread on the table," he said in a speech in June.
It is however possible Britain's labour market is nearing a turning point, and some of the post-crisis factors bearing down on wages are beginning to ease.
The number of workers on zero-hour contracts has fallen in the past six months, employers report increased skills shortages and some recruiters are finding they must offer big pay rises to tempt candidates.
The effect of a weaker pound since the Brexit referendum in June 2016 and concerns about Britain leaving the EU make this a particular issue for sectors such as construction that rely on foreign workers.
"We'll advertise for people and unless we put these increased rates on the advert, people won't reply," said Simon Noakes of Bespoke Recruitment, who now offers bricklayers 210 pounds ($269) a day, up from 160-170 pounds last year.
But official data show wage growth in the construction sector as a whole is slowing, and CIPD analyst Davies said trends in recruiters' day-rates and starting salaries did not give a good steer on future moves in average wages.
Moreover, faster wage rises will not be sustainable until British productivity growth improves its dismal post-crisis trend. Output per hour has stagnated since 2008, compared with an average of 2 percent a year before the crisis, and is closely correlated with wage trends.
"I can't overstate the significance of this underlying factor behind disappointing (pay) growth," Davies said. "Investment is not increasing in terms of skills or capital and machinery. Until that happens ... employers won't be able to afford the two percent plus pay increases that we all want." ($1 = 0.7805 pounds)
(Editing by Timothy Heritage)