* First half profit up 4.8%

* Raises 2023/24 profit forecast to 875 mln stg

* Sees inflationary pressures easing in 2024/25

* Softening labor market may impact demand in 2024/25

* Shares up 2.6%

LONDON, Sept 21 (Reuters) - British clothing retailer Next cautioned a softening in the labor market could dent consumer demand in 2024, taking the shine off a third profit upgrade in four months for its current financial year.

Britain's consumers have largely defied high inflation, which peaked at 11.1% in October, and rising borrowing costs to keep up their spending in 2023, helped by the strength of a labor market which is now showing signs of cooling.

Official data published last week showed the UK unemployment rate rose, the number of people in work fell sharply and vacancies dipped below 1 million for the first time in two years.

Next, which trades from about 500 stores and online and is often considered a gauge of how British consumers are faring, said on Thursday it was likely that inflationary pressures on selling prices and operating costs would continue to ease in its 2024/25 year.

But it cautioned that while a softening labor market may reduce pressure on wage inflation, it may also dampen growth in consumer demand in 2024/25.

"I'm not going to try and predict exactly what effect (a) softening employment market will have on demand, all we can say is one way or another it must weaken it," CEO Simon Wolfson told Reuters in an interview.

For the full year to January 2024, Next said it now expected a pretax profit of 875 million pounds ($1.08 billion), up from a previous expectation of 845 million and from the 870.4 million it made in 2022/23.

It also raised its guidance for full price sales growth to 2.6% from 1.8%.

For the six months to July 29, Next made a pretax profit of 420 million pounds, up 4.8%, on full price sales up 3.2%.

Its shares were up 2.6%, extending 2023 gains to 26%.

While industry data showed consumer spending lost pace last month, Next's rivals Marks & Spencer and Primark owner AB Foods have both raised their profit outlooks in recent weeks.

Next is considered by analysts to be one of the best run retailers in the country, having navigated both the pandemic and the cost of living crisis well.

It said its prices for autumn/winter will be up 2%, below a previous forecast of 3%.

For spring/summer 2024 it expects prices on like-for-like products to be between 0.5% up and 1% down.

($1 = 0.8120 pounds) (Reporting by James Davey; editing by Kate Holton, Jason Neely and Shron Singleton)