The U.K. is already putting out feelers about its future trading relations outside the European Union, which for more than 40 years has handled the country’s trade arrangements with the rest of the world.

The message British officials are delivering is one of a government committed to minimizing disruption to trade. As part of that, the U.K. is testing reaction to the idea that it will replicate the EU’s current schedule of tariffs to the rest of the world.

“That may facilitate things,” said Roberto Azevêdo, director-general of the World Trade Organization, in a January interview.

Yet the U.K. faces enormous hurdles in avoiding disruption to its own trade. And even if everything goes well, it will almost inevitably face reduced access to foreign markets immediately after it leaves the bloc, expected in just over two years.

That is largely because of the complexity of the task—and the interdependence of the several negotiating strands the U.K.’s new trade officials will have to pursue.

Not only will the U.K. need to work out its tariff schedule with the WTO, but it also must carve out a new trade relationship with the EU and a possible transitional deal to bridge to it. The WTO deal can’t be finalized until aspects of Britain’s agreement with the EU are known.

Some difficulties have been overblown. The U.K. is already a member of the WTO with all its rights and obligations. Its WTO negotiations may be complex, but they won’t be blocked, as some commentators have suggested, by political considerations such as Argentina’s dispute with the U.K. over the Falkland Islands or any Russian effort to thwart the process.

The WTO doesn’t work like that. Objectors must sustain a claim before a disputes panel that their trade has been harmed—in which case they, and only they, may secure the right to levy their own duties against the offender to offset the damage caused. There is no national veto that would prevent the U.K. from trading with the rest of the world.

But there are devils, for sure, in the detail. Other governments may be happy to accept the U.K.’s taking over the EU’s tariffs schedule, but there are other aspects to be agreed beyond tariffs. These include the levels of so-called trade-distorting subsidies Britain plans to support its own farms. There are also tariff-rate quotas, which are agreed amounts of sensitive products, such as lamb, beef and sugar, that can be imported under a lower tariff before the tariff rate jumps. These discussions, Mr. Azevêdo said, “will be trickier.”

The U.K. will need first to agree with the EU how much it takes of each tariff-rate quota, or TRQ—for example, what proportion each will take of the 228,254 metric tons of sheep meat New Zealand can now export at a zero tariff into the EU.  Then, having agreed that, the U.K. and EU will present their agreement to the other WTO members.There are about 30 bilateral EU agreements on TRQs; not all will be sensitive but some will be. In the talks, it may make sense to look at historical trade patterns—for example, the U.K. buys almost all the lamb New Zealand exports to the EU.

But it is quite likely other countries will object to losing any favored access to the EU-27—and it isn’t even clear other WTO members will concede to the creation of new TRQs with the U.K. This question alone suggests maintaining a positive U.K. relationship with the EU will be critical to both sides: Like the U.K., the EU could find itself the target of WTO complaints.

This is just a small part of their joint trade task in coming years. To minimize trade disruption, the EU and U.K. need a deep preferential trade deal, which under WTO rules has to cover “substantially all trade” between the two sides, and a likely interim arrangement to bridge to it.

The EU hasn’t yet formally conceded that trade talks can run in parallel with divorce proceedings, and officials insist the bloc wants some thorny questions, such as the U.K.’s Brexit bill, settled before talks can move on to other matters.

Trade experts say the U.K. should also try to seek continued access to the EU’s existing free-trade agreements with more than 50 countries. That would at the least need the agreement of the EU-27 and the other parties, and some European officials don’t see how that could happen once the U.K. steps out the EU’s customs union.

If these officials are right, the U.K.’s tariff-free access to other markets will shrink before increasing again once it strikes new preferential trade deals with other countries.

This will be happening amid the growth of other obstacles to trade with the EU, the country’s largest trading partner. Customs procedures and bureaucratic impediments to exporting will inevitably expand as the U.K. leaves the framework of common rules and regulations of the EU single market and customs union.