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The 'in' and 'out' camps both had support from 35 percent of respondents in the poll with 30 percent still undecided.
Support for both sides fell by 1 percentage point compared with a previous survey in March.
TNS also showed that people were becoming less sure about the likely outcome of the June 23 referendum with fewer people - 33 percent compared with 41 percent - now saying they expected Britain to remain in the bloc.
The number of people who thought Britain would leave remained stable at 28 percent but those who did not know what the outcome was likely to be rose to 38 percent from 31 percent.