The poll suggests that Usdaw, the shopworkers' union, is losing its influence on the Labour Party's Sunday trading policy. Kenneth Clarke, the Home Secretary, who is known to favour deregulation, needs the support of sympathetic Labour MPs to push through new legislation.
Nineteen per cent of Labour MPs in the survey support total deregulation with worker protection, or proposals advanced by the Shopping Hours Reform Council, which allow a significant extension of Sunday opening in England and Wales, with all stores allowed to trade for part of the day.
Another 10 per cent are divided between the Keep Sunday Special and Usdaw line, which opposes change, and the compromise solution proposed by the Shopping Hours Reform Council, which stops short of total deregulation.
The SHRC compromise also includes a right for shopworkers not to work on Sundays and premium pay for staff who do. Ian McGarrigle, news editor of Retail Week, said: 'Shopworker protection may be the price the Government will have to pay for reform.'
A Labour frontbencher said: 'I think the Government will get Sunday trading through. Worker protection will ease the way. If they offer worker protection, they will not get opposition from the Labour Party.'
Clive Betts, a Labour backbencher, said: 'They have got to offer premium pay otherwise there is a chance they will lose it.'
The Government is under pressure to act before Ray Powell's Private Member's Bill, backed by Keep Sunday Special, is debated in the Commons next January.