The GPC decided earlier this month that accepting the offer was the least damaging option.
LMC meetings held since the announcement have resulted in more GPs planning to accept.
Devon LMC chairman Dr Peter Jolliffe said 38 per cent were planning to reject the offer at a recent meeting of 400 GPs.
After seeing a presentation explaining the offer this figure dropped to 14 per cent. Acceptance of the DoH offer jumped from 64 to 82 per cent over the same period. Dr Jolliffe added: 'The resolution will probably influence GPs' opinion.'
Suffolk LMC's contract meeting was cancelled after the GPC released its latest guidance.
The GPC is to ballot UK GPs about the DoH's contract offer on extended hours. The poll closes on 29 February.
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