* UK business investment has lagged since Brexit

* "Largest business tax cut" in modern history-Hunt

* Tax break costs 11 bln stg a year

* OBR forecasts 3 bln stg a year investment boost

(Adds OBR details paragraph 5, BT reaction paragraph 7, IMF background paragraph 13, other reaction paragraph 16-20)

LONDON, Nov 22 (Reuters) - Britain's finance minister Jeremy Hunt made a tax break for business investment permanent on Wednesday, aiming to kickstart growth in the country's sluggish economy.

Britain has suffered from weak business investment since the Brexit vote in 2016, and economists blame the lack of corporate investment for the country's anaemic growth rate in recent years.

Hunt hopes that by making permanent the tax break known as "full expensing", companies will spend more on new kit and technology, lifting productivity.

"I will today make full expensing permanent. This is the largest business tax cut in modern British history," Hunt said in his Autumn Statement on Wednesday.

The move would boost annual business investment by around 3 billion pounds ($3.7 billion) a year, forecasts from the Office for Budget Responsibility (OBR) said.

More investment would help close the productivity gap with other major economies, the finance minister said, helping drive growth and raise living standards.

BT, a beneficiary of the tax break as it is investing billions in building a new fibre network, welcomed Hunt's move.

"It gives businesses like ours long-term certainty as we plan and build the country's digital infrastructure, and shifts the investment environment in Britain from good to great," Chief Executive Philip Jansen said.

The opposition Labour party, which is ahead of Hunt's Conservatives in the polls before an election expected in 2024, said it supported the move.

BREXIT DRAG

Full expensing is a capital allowance scheme that allows companies to deduct 100% of the cost of qualifying plant and machinery from their taxable profits.

Hunt said that the tax break costs the government 11 billion pounds a year. It was brought in earlier this year and had been due to expire in 2026, but the country's improved finances meant it could now be made permanent, Hunt said.

British business investment has trailed that of other developed economies, according to research from the International Monetary Fund.

In 2022, British business investment was slightly lower than its level in 2016, a contrast with other Group of Seven economies that experienced a 14% average increase during the period.

As well as the uncertainty caused by the 2016 Brexit vote, Britain has had four different prime ministers in seven years, creating a further headache for companies as they consider long-term decisions.

Manufacturing and engineering business group Make UK said Hunt's move was positive for business.

"The biggest factor that companies want when planning investment decisions is certainty in policy and this has now been provided by making full expensing permanent," Make UK boss Stephen Phipson said.

But the boss of car dealership chain Vertu Motors was less convinced.

"For many British businesses they're just trying to keep going. They're not investing heavily in plant and machinery," Vertu CEO Robert Forrester told BBC Radio earlier on Wednesday. "I don't think that's a massive, massive thing for most businesses." ($1 = 0.8025 pounds) (Reporting by David Milliken and Kylie MacLellan, writing by Sarah Young; Editing by Kate Holton and Alex Richardson)