LONDON, Dec 7 (Reuters) - Tesco Plc (TSCO.L), the world's No.3 retailer, said overseas markets drove a 7.2 percent rise in third-quarter sales and it was seeing a pick-up in demand in its main British market heading into the Christmas period.

The grocer, which trails French peer Carrefour SA (CARR.PA) and U.S. market leader Wal-Mart Stores Inc (WMT.N) by revenue, said on Tuesday sales at British stores open more than a year rose 1.5 percent, excluding fuel and including VAT sales tax, in the 13 weeks to Nov. 27.

Finance Director Laurie McIlwee said British growth picked up to 3 percent by the end of the third quarter and could improve further in coming weeks.

"It is hard to call what the fourth quarter's actually going to be, but I would say it is going to be an improvement quarter-on-quarter in terms of like-for-like (sales)," he told reporters on a conference call.

"We still feel there is good growth in the UK."

International retailers like Tesco are benefiting from a global economic recovery led by Asia. But chains in Britain, where Tesco makes about two-thirds of sales and profits, are worried tax hikes and public spending cuts aimed at reining in government debt could hit demand in coming months.

An industry survey on Tuesday showed British retail sales growth slowed in November.

Tesco, which runs more than 5,000 stores in 14 countries, said third-quarter sales rose 7.2 percent excluding fuel and at constant exchange rates.

That included an 11 percent rise overseas. As well as good growth in Asia, Tesco reported a 9.8 percent increase in like-for-like sales in the United States and underlying growth in all its European markets for the first time in three years.

British underlying sales, adjusted for changes in VAT sales tax, were up by between 0.7 and 0.8 percent, McIlwee said.

That was ahead of the average forecast for a 0.3 percent increase, according to a Reuters poll of 12 analysts, and compares with recent quarterly rises of 1.3 to 2.1 percent at British rivals Asda, Sainsbury (SBRY.L) and Morrison (MRW.L).

Some analysts think Tesco is suffering relative to British rivals because it sells more discretionary non-food goods.

McIlwee said non-food sales rose 3 percent in the third quarter, including a 30 percent surge at its online Tesco Direct business and an increase on a like-for-like basis.

Tesco shares have lagged the STOXX Europe 600 retail index .SXRP by 7 percent this year. They closed on Monday at 420 pence, valuing the company at 34 billion pounds ($53 billion).

By Mark Potter

(Additional reporting by James Davey; Editing by David Holmes) ($1 = 0.6382 pound)