British Nationals do not require a visa for stays up to 30 days, however you can extend this for up to 90 days by applying at an Immigration Office. Your passport should be valid for at least 6 months from the date of entry into Honduras.
Children travelling with only one parent or without both parents must present a notarised letter of consent from the non-travelling parent(s) to enter and exit Honduras.
There is an airport departure tax, which is usually included in the airfare. Check with your airline to confirm this.