* Dollar index languishes near recent 6-1/2 month low

* Sterling dips after poll shows slimmer lead for PM May

By Masayuki Kitano

SINGAPORE, June 1 (Reuters) - The dollar languished near a recent 6-1/2 month low against a basket of major currencies on Thursday, while sterling slipped after a poll showed a slimmer lead for Prime Minister Theresa May's ruling party before next week's election.

The latest YouGov poll for the Times on Wednesday showed that May's Conservative Party is just 3 percentage point in front of the opposition Labour Party ahead of Britain's June 8 election.

That weighed on sterling, which slipped 0.1 percent to $1.2875.

The pound was just above a one-month low of $1.2770 set on Wednesday, having regained some ground after two other surveys showed May's poll lead in double digits, countering signs she might fall short of a majority in next week's election.

The greenback licked its wounds, suffering its biggest monthly drop in four months against a basket of six major rivals in May, and its largest loss against the euro in more than a year.

The euro eased 0.1 percent to $1.1236. On Wednesday, the euro had risen 0.5 percent, bringing it back near last week's 6-1/2 month high of $1.1268.

A drop in U.S. bond yields on Wednesday pressured the dollar, said Satoshi Okagawa, senior global markets analyst for Sumitomo Mitsui Banking Corporation in Singapore.

"U.S. longer-term bond yields fell and that led to some broad selling of the dollar," Okagawa said.

Currently, futures markets are pricing in a roughly 90 percent chance the Federal Reserve will raise rates by 25 basis points in June, but much could change depending on economic data in the run-up to that meeting, most notably Friday's jobs report.

The dollar index, which measures the greenback's value against a basket of six major currencies, last traded at 97.035 , not very far from its May 22 trough of 96.797, which was the lowest since Nov. 9.

In May, the dollar index fell 2.1 percent, its biggest monthly drop since January.

Investors have been fretting that investigations into U.S. President Donald Trump's ties with Russia could hamper his administration's progress on tax cuts and other promised stimulus measures, concerns which have weighed on the dollar in recent weeks.

The dollar edged up 0.1 percent against the yen to 110.95 . (Reporting by Masayuki Kitano; Editing by Shri Navaratnam)