EU-Citizen with Non-EU Family

[Any]

I am an EU-Citizen outside my country of citizenship. I live in South America and never worked in an EU country.
In the event that I move to the UK, will my husband and children (non-EU citizens) need to apply for a Family Permit before we travel, or we will they be able to enter with me and later on apply for the permit?
I understand that the topic must have been explained before, but there is no British Consulate in the country we currently live, and we have not been able to get proper answers at the nearest Consulate, although we have sent many emails and called several times.
I have already filled an on-line form but I do not have a National Insurance Number, so I can not make any progress or even set an appointment at the nearest Consulate.
Any advice will be highly appreciated. Thank you in advance.

[Mr Rusty]

What nationality are your family? Do they require a visa to travel to the UK?
If they don't, e.g. Brazilian or Argentine nationals, then they can travel here and sort out their status in the UK. Best not to try and deceive the Immigration Officer when you arrive by pretending to be visitors. Their instructions are that EEA Family Members without a Permit should not be refused entry without being given the opportunity to prove their status. So carry essential documents like marriage certificate, birth certificates etc. They will probably grant entry for a couple of months so that you can apply to UKBA, or at worst grant Temporary Admission and refer the case themselves. I think it's extremely unlikely that your family would be sent back.
If they do require visas to travel here, e.g. Colombian, then you'll have to apply for the Family Permits anyway. The good news is, applications are free of charge.

[Any]

Thank you for your prompt response!
My husband and children are Paraguayans and we have been told that no visa is required, so apparently they will be allowed to enter as my family, and once settled, apply to UKBA; is that correct?
I really appreciate you help!