The Tunbridge Wells and Tonbridge MPs have seen their constituencies placed into Tier 3 along with the rest of Kent.
They were among 55 Conservatives who voted against the Government as Parliament was asked to approve the three-tier system, which comes into force today.
The measures, aimed at slowing the spread of coronavirus, were passed by 291 to 78, but another 16 Tory MPs abstained, including Nus Ghani, whose Wealden constituency in East Sussex has been classified as Tier 2.
Mr Clark and Mr Tugendhat were among seven Kent MPs who had pressed the Health Secretary, in a joint letter, to base the tier system at a district and borough level.
They have argued that areas such as Tunbridge Wells, which has the lowest infection rates in the county, shouldn’t be compared to places such as Swale or Thanet where Covid levels remain high.
Tier 3 restrictions will see many pubs, restaurants, hotels and entertainent venues such as theatres forced to stay shut until at least December 16 when the Government has promised to review the tier classifications.
Last night’s vote was the largest backbench rebellion of Boris Johnson’s premiership, but the motion was passed after all opposition parties, including Labour, abstained.