It would depend upon where you changed flights, and the corresponding layover times. See Wikipedia for possible changing points:
http://en.wikipedia.org/wiki/Eduardo_Gomes_Int ernational_Airport
Delta fly from Gatwick to Manaus, via Atlanta. A quick look at their website offers a flight of 9 hours 50 minutes to Atlanta, a 3 hour layover in Atlanta, and 6 hour 22 minute flight to Manaus, making
19 hours 12 minutes in total.
http://www.delta.com
That's probably the quickest way from Gatwick, since there don't appear to be any suitable flights directly into South America:
http://www.gatwickairport.com/portal/page/Gatw ick%5EGeneral%5EFlight+information%5EDestinati ons+and+airlines/
An alternative route might be to fly from Heathrow to Manaus, via S�o Paulo, with TAM:
http://www.tam.com.br
Chris