The correct term would be Money Bill as defined below in the Parliament Act. It should be noted that the actual Finance Bill/Act, which is the Budget, is not normally declared to be a Money Bill. I don't think the term Welfare Bill has any defined meaning.
"A Money Bill means a Public Bill which in the opinion of the Speaker of the House of Commons contains only provisions dealing with all or any of the following subjects, namely, the imposition, repeal, remission, alteration, or regulation of taxation; the imposition for the payment of debt or other financial purposes of charges on the Consolidated Fund, the National Loans Fund or on money provided by Parliament, or the variation or repeal of any such charges; supply; the appropriation, receipt, custody, issue or audit of accounts of public money; the raising or guarantee of any loan or the repayment thereof; or subordinate matters incidental to those subjects or any of them. In this subsection the expressions "taxation," "public money," and "loan" respectively do not include any taxation, money, or loan raised by local authorities or bodies for local purposes.[3]"