Of course Philip Hammond supports the Customs Union, and a great deal more than that. Theresa May is a Remainer sitting for Remainer Berkshire, and Hammond is Remainer sitting for Remainer Surrey.
The Conservatives are concentrated heavily in the Remainer heartlands of the South, and they are starting to feel the breath of the Lib Dems on their necks. The Lib Dems are unlikely to win Maidenhead (these days), or Runnymede and Weybridge, but there are plenty of far lower-hanging fruit within a very short distance of those.
Never mind the Conservative Right. Neither Jacob Rees-Mogg, who on Windrush has turned out not to have been all that right-wing after all, nor Peter "The Brexit Queen" Bone, is ever going to be the Minister for anything, and Philip Davies, on the outermost fringe of political life, has always stood even less chance than they did. In any case, he is practically certain to lose his seat.
Even Amber Rudd was sacked for being insufficiently liberal, and the next Leader will be the next Remainer in line, without an election, because that is how the Conservative Party works. The Right has nowhere else to go, and it is unlikely to have a sizeable presence in the next Parliament. It has only a fairly small presence in this one, which is why no one who matters pays any serious attention to it.