Vettel's championship advantage halved following tense battle between fierce rivals at Spa.
Hamilton set a new track record to fend off the on-form Vettel.
Vettel's contract with Ferrari expires at the end of the season but Hamilton is adamant he would not join Mercedes.
Mercedes were left shocked when Rosberg walked out of F1 in December last year after winning the title a week earlier.
F1 currently hosts street race in Singapore but wants to grow further in the continent.
Raikkonen's teammate Vettel's current contract with Ferrari expires at the end of the 2017 season.
Ferrari recorded their second one-two finish of the season in Hungary - the first was in Monaco.
Mercedes are currently 39 points ahead of Ferrari with nine races still to go this season.
Spaniard hasn't finished on the podium since returning to McLaren in 2015.
Hamilton is 14 points behind championship leader Sebastian Vettel with nine races to go.
Vettel struggled with steering while Hamilton failed to overcome Ferrari duo.
Hamilton closed the gap to Vettel to just one point in the Drivers' Championship after Silverstone win.
Hamilton admitted earlier that he could hang up his helmet at the end of the current campaign.
The Halo device was extensively tested by all the teams in 2016.
Hamilton is currently just one point behind championship leader Sebastian Vettel with 10 races to go.
Hamilton reduced the gap in the drivers' championship to just one point.
Sebastian Vettel and Kimi Raikkonen both suffer late punctures as Valtteri Bottas secures Mercedes one-two.
Lewis Hamilton has taken pole in Silverstone.
Valtteri Bottas will be demoted five places after Mercedes were forced into an unscheduled gear box change.
Hamilton skipped F1's first-of-its-kind event to engage fans in London ahead of the British GP.
Hamilton will look to close the 20-point gap with Vettel at his home race.
Hamilton is 20 points behind championship rival Vettel going into the midway point of the 2017 season.
Final race at famous Northamptonshire circuit could come in 2019 if no new agreement can be reached.
Sergio Marchionne says there is no prospect of the two-time world champion returning to Maranello.
Mercedes driver claims second race win after claims of a jump start.
Valtteri Bottas has taken pole in Austria with Hamilton starting in eighth.
German escapes reprimand for actions in Azerbaijan after FIA hearing in Paris.
Duo's previously friendly relationship looks set to deteriorate after controversial collision in Azerbaijan.
Ferrari driver now has nine penalty points on his license - three more would result in a one-race ban.
Vettel and Hamilton finished fourth and fifth respectively with Daniel Ricciardo winning in Baku.