* EU workers shunning British jobs - Hays CEO
* Finance firms not moving significant job numbers out of UK
* First half operating profit up 16 pct, beats consensus
* Shares fall 5 pct after strong rally in year to date (Recasts with CEO, adds analyst comments, details, shares)
Feb 22 (Reuters) - British construction sites are starting to see a labour shortage as Eastern Europeans, who have traditionally filled the bulk of on-site jobs, have stopped taking positions after Britain's decision to leave the EU, recruiter Hays said.
Chief Executive Alistair Cox said there was "less appetite" for non-British workers to take jobs following the Brexit vote and some European Union citizens had quit jobs in Britain, with the immediate impact being felt on construction sites.
"We are starting to see skill shortages in a number of areas there because of a lot of the traditional supply, much of which has come from Europe has dried up," he told Reuters.
Cox's comments are the first indication that firms may struggle to fill jobs after Brexit. So far, staffing companies had said employers in Britain had frozen new job investments and were only hiring replacements for jobs being vacated.
The concern remains that Brexit could cause a mass-exodus of jobs to other countries with large European agencies vacating their British headquarters and financial companies detailing plans to transfer jobs to keep servicing EU clients.
Finance firms had begun moving "some small areas of the business" with "relatively insignificant numbers" of jobs to other European countries, Cox said, declining to name the companies or the functions of jobs moved.
But he said there had not been any moves of larger departments or "hundreds or thousands" of jobs and said finance firms were not only hiring replacements for those leaving but also making fresh hires for risk, compliance and audit.
Hays said the wider British market, which along with Ireland accounts for about a quarter of the group's net fees, remained subdued but stable. Cox also said that wage inflation remained subdued at about 2 to 2.5 percent a year.
Profit from Britain and Ireland rose 24 percent to 22.6 million pounds in the six months ending Dec. 31, helped by cost controls. Like-for-like net fees grew 1 percent.
This improvement and international growth pushed Hays' profit up 16 percent to 116.5 million pounds ($161.7 million) beating consensus of 115.6 million pounds.
Three analysts said they expected full-year profit consensus of 239.8 million pounds to rise by low single digits, but Hays' shares, up about 12 percent this year, fell 5 percent at 194 pence at 0819 GMT, a steeper fall than the midcap index.
"Shares have been strong coming into the earnings and probably are already pricing in the upgrades," Morgan Stanley analysts wrote.
($1 = 0.7205 pounds) (Reporting by Esha Vaish in Bengaluru; Editing by Gopakumar Warrier and Edmund Blair)