Britain has signed a post-Brexit trade deal with the Pacific islands of Fiji and Papua New Guinea, as the government rushes to sign as many agreements as possible before 29 March.

The Department for International Trade said the agreement would maintain access to goods including sugar and fish imported from the islands 10,000 miles away. Total trade between Britain and the region is worth about £369m a year.

Signed by the international trade secretary, Liam Fox, the deal eliminates all tariffs on all goods imported from Fiji and Papua New Guinea and will gradually remove around 80% of tariffs on UK exports to these countries.

It comes only a day after the government said it would slash tariffs to zero on the vast majority of imports to Britain under a no-deal Brexit, rendering the deal less significant for UK consumers.

The Pacific islands deal is part of the UK’s pledge to support developing nations and use trade to reduce poverty, but it also comes as ministers rush to sign deals with about 70 countries the UK trades with under EU free trade agreements, which are due to end in two weeks’ time. Those agreements would, however, be rolled over if MPs approve Theresa May’s deal before 29 March or if Brexit is delayed through an article 50 extension.

Deals have been signed with nations including Switzerland, Chile and the Faroe Islands. Deals with major trading partners such as Japan, Turkey and South Korea are not expected to be ready in time, much to the alarm of business leaders. If there is a no-deal Brexit, trade with those countries would default to World Trade Organization terms.

The Pacific islands deal also comes days after the EU added Fiji to a tax haven blacklist. Tonia Antoniazzi, a Labour MP campaigning for a second referendum, said it was a “pathetic return on Fox’s promise of easy trade deals”.

“The EU is the destination for the majority of British trade, so trade continuity deals with Fiji and Papua New Guinea don’t cut the mustard,” she said.

Fox said: “I am delighted to sign this trade continuity agreement today as it will allow businesses to keep trading as freely as they do today, even in a no-deal scenario.”