MILAN/LONDON, Feb 14 (Reuters) - TUI has become the latest company to ditch the London stock market, which is struggling to retain big companies and attract new share offerings, after shareholders of Europe's biggest travel agent voted to move its listing to Frankfurt.

The go-ahead at Tuesday's annual general meeting to focus on a Frankfurt listing comes two weeks after London-listed gambling firm Flutter said it would propose moving its primary listing to New York at its shareholder meeting in May.

TUI also reported far better-than-expected quarterly results as it swung to a profit on the back of robust travel demand.

Other big firms have also left London in recent years, or are considering leaving, under pressure from investors seeking to boost the value of their shareholdings following Brexit-related complications that have squeezed UK market valuations.

"We see a lot of dissatisfaction among management of UK companies that are continuing to grow and where their share prices just don't reflect that," said David Stevenson, who manages portfolios of small- and mid-cap UK companies at Amati Global Investors in Edinburgh.

"It's tough love for many companies (listed in London). Some grumble about it, some vote with their feet, and it's not a healthy environment at all," he said.

According to LSEG data, UK stocks are currently 35% cheaper than their global peers, almost the widest gap in more than three decades. Before Britain's vote to leave the European Union in 2016, the UK market commanded a slight premium.

The UK market for initial public offerings has also been slow in the last year. British chip maker ARM Holdings opted to list in New York and since its September flotation its shares have trebled. British commodities broker Marex Group also plans to list in New York rather than London.

Against this backdrop, UK regulators have begun tweaking EU-designed rules to try to boost London's global competitiveness, including listing rules and what insurers can invest in. But financial leaders have called for faster progress.

TUI has said its delisting from the London Stock Exchange is expected in June. That would pave the way for an upgrade of its Frankfurt listing to the Prime Standard market segment and inclusion in the mid-cap MDAX index. Its shares were highly volatile on Tuesday but ended little changed in Frankfurt and London, keeping their one-year declines at over one third. Over 98% in the shareholder vote backed the London delisting.

A growing number of UK-listed companies are favouring a U.S. listing, where valuations can be higher.

Building materials company CRH moved its primary listing from London to New York in September, and the year before plumber Ferguson left the FTSE 100.

The London market has shrunk in recent years. The FTSE All-Shares index has a market capitalisation of $2.8 trillion, down almost 20% from June 2015, the year before the Brexit referendum, according to LSEG data.

Paris, Europe's largest stock market by value, is worth around $3.4 trillion and has grown by nearly 50% in that time. (Reporting by Danilo Masoni in Milan and Naomi Rovnick in London Additional reporting by Joanna Pluciska Editing by Amanda Cooper and Mark Potter)