The Isles of Scilly's MP voted in favour of yesterday's motion supporting the Prime Minister's negotiating strategy.
Theresa May lost the largely symbolic vote by 303 to 258, with many Tories in the Brexit-backing European Research Group abstaining.
Derek Thomas wrote on his website that he supported the February 14th motion, describing Mrs May's deal "as the most achievable route to ensure a smooth exit" from the EU on March 29th.
He wrote: "I voted for the motion as it reaffirms Parliament's support for the Government to find alternative arrangements for the backstop, to avoid a No Deal. The motion was defeated by 45 votes.
"Theresa May is currently holding cross party talks and negotiating with the EU on the withdrawal agreement, particularly the backstop.
"Whilst MPs, including myself, have concerns about Theresa May’s deal (the Withdrawal Agreement) it provides the most achievable route to ensure a smooth exit from membership of the EU on March 29th. This view is widely shared in Parliament and, I suspect, in the country at large, save for the concerns, which I share, about the Northern Ireland/ Ireland backstop.
"I have consistently said that I believed a withdrawal agreement could secure the support of enough MPs if concerns over the backstop could be addressed.
"It is for Parliament, not Brussels, to decide when we fully leave the EU. If Brussels are prepared to honour the result of the referendum and are determined to avoid a No Deal, negotiators would do well to support the Malthouse Compromise."
Derek recently apologised for the Government and MPs failing to respond to the needs of the British people due to the distractions of Brexit.