There will be no change to the rights and status of EU nationals living in the UK, nor UK nationals living in the EU, while the UK remains in the EU.
Although there is no recent history of terrorism in Latvia, attacks can’t be ruled out. See Terrorism
Around 65,000 British nationals visit Latvia each year. Most visits are trouble-free.
If you’re abroad and you need emergency help from the UK government, contact the nearest British embassy, consulate or high commission.
Take out comprehensive travel and medical insurance before you travel.