Following on from their International Challenge Trophy Group A defeat in Slovakia, England were under pressure from the start, conceding four corners inside the opening 10 minutes.
Hungary pushed forward at every opportunity, but Franks and his team-mates held firm and began to get into the game too.
However, the hosts took the lead on 37 minutes when the impressive Bobal fired home from 20 yards.
It was 2-0 just before the break too when a cross from the right was headed home by the unchallenged Mervo.
England could have found themselves in an even worse scenario when Varga picked up a loose ball and surged forward seconds later, but was denied by a fine save from Andy Coughlin.
Boss Paul Fairclough made five changes at half time, and England were back in the game on 52 minutes when Matty Pearson netted fter latching onto Elliot Frear’s through-ball.
The Three Lions pushed for an equaliser, but were caught out eight minutes later.
A counter-attack left three defenders appealing for offside which wasn’t given allowing Varga to slide the ball home at the far post.
Back came England once more though as Frear won the ball out on the left wing and pulled it back for Matty Taylor, to sidestep his marker and score.
Hppes of a remarkable comeback were dashed five minutes from time when Lazlo Toth broke clear into the penalty area and lifted the ball over the advancing Coughlin.
Afterwards, Fairclough said: “Whilst the opposition were technically more adept than us, the team spirit of the side refused to give in.
“At 2-1 and 3-2 we were very close to getting back into contention.
“We must now re-group for the remaining International Challenge Trophy fixtures.
“We know what we need to do against Turkey and Estonia if we wish to progress to the semi-finals and it is down to myself to make sure that we are fully prepared.”
Franks will be unavailable the next time England C are in action as selection is only available for non-league players.
England C: Andy Coughlin (Wrexham); Angus Macdonald (Salisbury City FC), David Fitzpatrick (Southport), Marc Roberts (FC Halifax Town), Josh Payne (Woking); Fraser Franks (Luton Town), James Marwood (Gateshead), Jake Gallagher (Welling United), Matty Taylor (Forest Green Rovers); Danny Bradley (Barnet), Marcus Maddison (Gateshead).
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