LONDON (Reuters) - European Union lawmakers on Tuesday gave broad support to a law that could end the City of London s global dominance in clearing euro-denominated financial contracts after Brexit. The plan has raised hackles in Britain, where it threatens both job losses and tax revenues. The draft EU law proposes that a foreign clearing house   which stands between two sides of a transaction to ensure its smooth completion   must be subject to more intense supervision by the bloc s regulators if it wants to serve customers in the EU. But if a clearing house is systemically important to the euro zone, then euro-denominated business with EU based customers must move to the bloc. The draft law is anathema to Britain, which voted to leave the EU in a referendum last year. It is home to LCH, an arm of the London Stock Exchange that clears most euro-denominated swaps in Europe. Financial services represent Britain s biggest tax earning sector and the LSE has warned that thousands of jobs could leave the UK if euro clearing was forced out. In the first debate in the European Parliament on Tuesday, lawmakers from the two biggest parties, the center right European People s Party and the center-left Progressive Alliance of Socialists and Democrats, gave broad backing to the draft law, but called for some changes.  It s a good proposal from the European Commission,  Polish center-right MEP Danuta Huebner told parliament s economic affairs committee.  In principle, I support the proposal, which I find necessary,  added Roberto Gualtieri, an Italian center-left lawmaker who chairs the committee. The European Parliament and EU states have final say on the reform, with changes expected during the approval process. No timetable has been agreed for approving the law and, separately, there has been scant agreement on any new relationship between the EU and Britain. That means LCH s European customers don t know at the moment if they can continue using the London clearer after Brexit. Exploit this uncertainty, Frankfurt-based Eurex unveiled a  Brexit-proof  package of sweeteners on Monday to woo LCH customers. Huebner said parts of the draft law were too complex, creating uncertainty over how exactly EU regulators and the European Central Bank would decide when euro clearing conducted outside the bloc must move to the EU.  We have to do everything to avoid potential inconsistency in decision-making,  Huebner said.  We must not politicize the whole process.  Gualtieri said there was a need to  upgrade  EU supervision of clearing, but lawmakers should be  very cautious, reflective and in a listening mood  given the potential consequences. Others said there was need to avoid protectionism or using clearing as a stick to beat Britain given that the UK was already  fighting with itself . Kay Swinburne, a British center-right lawmaker, a lone voice in outright opposition, said a regional restriction on a global currency is the wrong approach.  There is a reason why we have done so much work at the global level, and I really hope that we are not going to throw all of that away to have some protectionism with regards to a Brexit decision,  Swinburne added. Banks and the LSE have warned that forcing out some clearing would split markets and bump up costs for EU companies who use swaps to insure against adverse moves in borrowing costs, raw material prices, and currency swings. 