A useful list of which countries are welcoming foreign visitors, and which still have restrictions.
Most countries require a negative Covid test and completion of a passenger information form, and some ask for evidence of vaccination. The FCDO website (www.gov.uk/foreign-travel-advice) has a clear summary of country entry requirements in more detail.
Fully open, no significant restrictions
Brazil, Colombia*, Costa Rica*, Ecuador/Galapagos, El Salvador, Guatemala, Guyana, Honduras, Nicaragua, Mexico*, Paraguay, Peru
*no pre-arrival test required
Open, but with significant restrictions
Bolivia (quarantine), Cuba (arrival test and quarantine), Falkland Islands (quarantine), Panama (quarantine for UK citizens), Venezuela (test on arrival)
Not yet open
Argentina (due to open on 1 November), Chile (opening 1 November), Uruguay (opening 1 November)
Updated 8 October (Guatemala moved to fully open section)