* New UK govt looking for EU food and veterinary deal

* Minister says European Court of Justice role to be decided

* Britain cautious on imposing tariffs on China EVs

* London looking to resume India trade talks

ROME, July 16 (Reuters) - Britain's new trade minister said on Tuesday he was optimistic some trade barriers with the European Union can be removed, but the mechanism to arbitrate any disputes would be subject to negotiation.

The Labour Party won a July 4 election, and while it has pledged not to reopen the core pieces of Britain's deal to leave the European Union, it is aiming for a new food and veterinary agreement to reduce border checks on animal products.

Critics say that will mean accepting oversight from the European Court of Justice (ECJ), a red flag to Brexit campaigners who see it as an infringement of British sovereignty.

Speaking in Italy where he had attended a meeting of fellow Group of Seven (G7) trade ministers, Britain's newly installed secretary of state for business and trade, Jonathan Reynolds, said that he believed there was "space" for a deal and did not rule out having to turn to the ECJ for eventual arbitration.

"How you resolve any dispute is always something that will be a part of the negotiation you are having," he told Reuters, speaking by telephone from the southern region of Calabria.

"Of course this is one facet of a deal that we hope will cover a whole range of issues, not just economic but also relating to defence and security as well," he said.

He also confirmed that he wanted to secure the mutual recognition of certain professional qualifications with the 27-nation EU bloc, and easier access for musicians on tour.

Reynolds said during his brief trip to Italy he had discussed with European colleagues an EU move to impose tariffs on the imports of China-built electric vehicles to counter what Brussels believes are unfair subsidies for Chinese firms.

However, he sounded cautious about the prospects of Britain following suit, saying the domestic auto sector was export-driven and that British firms had not complained about China.

"I am not ruling anything out, but if you have a very much export-orientated industry, the decision you take (has to be) the right one for that sector," he said.

RESUMING INDIA TALKS

The previous British government pursued a range of trade deals since it left the European Union, but talks with Canada stalled in January, while talks with Delhi were put on hold this year ahead of the Indian elections.

Reynolds said he had "an excellent meeting" with the Canadian delegation at the G7 meeting, but added: "We have not, at this stage, formally agreed to reopen talks."

India's Trade Minister Piyush Goyal also attended the G7 conference and invited Reynolds to visit India. No date had been set, but the British minister said he hoped to resume negotiations with India "as soon as possible".

Reynolds acknowledged that Britain was unlikely to secure a bilateral trade deal with the United States any time soon, but predicted that relations would remain warm whoever won presidential elections in November.

"The U.S. will always be a key relationship for the U.K. regardless of the political leadership of these countries," he said. (Additional reporting by Alistair Smout in London; Editing by Keith Weir)