LONDON (Reuters) - British new car registrations rose modestly in May while private and business demand fell, possibly reflecting uncertainty over Britain's European Union referendum, the Society of Motor Manufacturers and Traders said on Monday.

Registrations overall rose 2.5 percent in May to 203,585 units, SMMT said in a monthly update.

"The new car market in May remained high ... but the low growth is further evidence of the market cooling in the face of concerns around economic and political stability," SMMT chief executive Mike Hawes said.

Fleet buyers drove growth, with demand up 8.8 percent, while registrations by private customers were down 3.0 percent and the business segment fell by just over 20 percent.

"Whether this is the result of some buyers holding off until the current uncertainty is resolved or a sign of a more stable market for new cars remains to be seen," Hawes said in a statement.

In April, new car registrations rose by 2.0 percent.

Britain's economy has slowed ahead of the June 23 referendum on the country's EU membership. Earlier on Monday, a group representing British manufacturers said they expected a slight recovery for the sector later this year but that slow improvement could be knocked off course if the country votes to leave the EU.

(Writing by William Schomberg; Editing by Toby Chopra)