British bookmaker William Hill says it's offering an "In" vote at the shortest odds since the date of next month's referendum on European Union membership was announced in February.

Odds on "In" had shortened to 1/6 on Monday, implying an 85 per cent chance of the country deciding to remain in the EU, compared with 1/5 (83 per cent) previously.

"Out" was at the longest odds yet at 4/1 (20 per cent) from 10/3 (23 per cent).

On February 20, the day the referendum date was confirmed, Hills offered 2/7 "In" and 5/2 "Out".

A spokesman for William Hill said 79.2 per cent of all the stake money taken was for "In" but 64.4 per cent of individual bets struck have been for "Out".

As opinion polls have given sharply different pictures of the public mood, many investors are watching betting odds closely.

Odds have consistently indicated a high probability of an "In" result in the June 23 referendum.