The body is currently assisting on 300 live police operations targeting modern slavery, with alleged victims as young as 12 being sold to families in the UK from Europe.
Will Kerr, NCA director of vulnerabilities, said: "The more that we look for modern slavery, the more we find evidence of the widespread abuse of the vulnerable.
"The growing body of evidence we are collecting points to the scale being far larger than anyone previously thought.
"This should not be acceptable in any way, shape or form."
Mr Kerr's comments come as the NCA launches an advertising campaign raising awareness of the signs of modern slavery in everyday life.
He said there were "lots of different outlets" for people trafficked into the UK to be working illegally and against their will, with many affecting people in everyday life.
Mr Kerr said examples included those working at car washes and in construction as well as in agriculture and food processing - often receiving very little pay and forced to put up with poor living conditions.
Others sold into slavery could be kept in pop-up brothels, where sex workers promised a better life are left penniless with few clothes other than underwear, while some can be working at cannabis factories, he added.
"As you go about your normal daily life and as you're engaged in a legitimate economy accessing goods and services, there is a growing and a good chance you will come across a victim who has been exploited in one of those different sectors," he said.
"That's why we are asking the public to try and recognise the signs and to report their concerns and suspicions to us."
He said signs of slavery included visible injuries, a distressed appearance and any indication they are being controlled by another person.
Anyone with information about possible slavery gangs is asked to contact the NCA on 08000 121 700.