In fact, historically, few right wing parties in Europe in general have opposed welfare programs outright. A large portion of European welfare programs came from the centre right or right, partially on the basis of a Christian morality argument (e.g. Bismarcks original German healthcare and pension insurance reforms, backed by Zentrum, a party who went on to support Hitlers candidacy for Chancellor, and whose spiritual successor is the CDU), partially as a realisation it was either forging compromises or risk revolution (e.g. Bismarks reforms were at least in part outright "stolen" from demands from left wing parties he banned and imprisoned leading members of, as part of a two-prong strategy of appeasement and an iron fist.

That free market and right libertarian parties have gained some traction again is a relatively "new" (few decades) phenomenon, after many of them were squeezed hard by the rapid growth of socialist parties to their left a century ago.

EDIT: Worth adding that classically liberal parties in Europe have largely leaned socially liberally, e.g. "low overhead welfare" rather than no welfare. A lot of the universal basic income talk comes from classical liberals as a counter to social democratic "big government welfare" not by removing the welfare but by trying to minimise government involvement in the equation.