The private member's bill, put forward by fellow Tory Rebecca Harris, urges the government to launch a study of the pros and cons of moving the UK's clocks forward a hour throughout the whole year not just during the period of British Summer Time (BST).
It recommends ministers should conduct a trial of moving to BST, which last happened between 1968 and 1971.
'Customary time' Mr Rees-Mogg, who opposes the bill, has tabled an amendment to the proposed legislation suggesting "the county of Somerset as defined by the Lieutenants Act shall revert to the customary time used prior to the Great Western Railway time established in 1840".
Before the 1840s, times were set locally across the country, often by churches, based on the position of the sun.
This meant that the time in Plymouth was about 20 minutes behind London, which followed Greenwich Mean Time.
This practice effectively ended when the Great Western Railway introduced a standardised timetable for its trains.
Railway firms' move to standardised timetables - pegged to GMT - in the 1840s and 1850s were initially resisted with large towns continuing to show both "railway and local time" separately.
Parliament passed a law in 1880 to make GMT the standard time across the UK.
'Flawed' Mr Rees-Mogg told BBC Somerset he had tabled the amendment because he wanted MPs to discuss all the issues involved in whether the UK should move to a different time zone.
And referring to past calls by some politicians in Scotland for it to adopt separate arrangements from the rest of the UK, he said: "If it's good enough for Scotland, it's good enough for Somerset."
Mr Rees-Mogg told the
Politics Home website recently that the bill was flawed "as you can't create more hours".
The coalition government has said it is prepared to listen to arguments about putting the clocks forward all year-round but the move is opposed by MPs in Scotland and the north of England who are concerned it would extend hours of darkness in the morning and lead to more accidents.
Mr Rees-Mogg, who was elected to Parliament for North East Somerset in 2010, recently suggested that council officials seeking to impose on-the-spot fines for minor offences should be forced to wear bowler hats.
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