However, even a win looked unlikely when they trailed 13-3 at the break and only Britton's try and some timely goalkicking from Bath's Tom Heathcote saved the day.
After an early Heathcote penalty sailed wide, Australia were first on the board through the boot of Kyle Godwin to make it 3-0 before Heathcote levelled the score with 12 minutes on the clock.
Godwin again put three on the board for the men in Green and Gold and could have extended the lead further but missed his next two attempts on goal after England were penalised at the breakdown.
In wet conditions both sides lacked discipline in key areas and with 25 played Heathcote had the chance to level the scores but saw his kick miss the posts.
Australia got the first try of the game just before the break, good pressure on the England line was eventually rewarded when captain Liam Gill went over to score.
But Hunter's side started the second half with fire in their bellies. First Heathcote kicked over three points before the pack showed good strength for hooker Britton to touch down for his first England Under 20 try to make it 13-11 after 49 minutes.
England wing Marland Yarde was sent to the sin-bin for being offside and the man advantage almost paid dividends for Australia but replacement back Nick Frisby was knocked into touch just short of the try line by a combination of Sam Hill and Heathcote.
With Yarde still in the bin England pushed on and two successful Heathcote penalties in quick succession gave England the lead for the first time in the match to make it 17-13 and the men in White held out for the win.
Points: Heathcote 4P; Britton 1T.
England Under 20 starting XV against Australia
15 Ben Ransom (Saracens)
14 Marland Yarde (London Irish)
13 Sam Hill (Exeter Chiefs)
12 Ryan Mills (Gloucester Rugby)
11 Charlie Walker (Harlequins)
10 Tom Heathcote (Bath Rugby)
9 Dan Robson (Gloucester Rugby)
1 Alec Hepburn (London Wasps)
2 Koree Britton (Gloucester Rugby)
3 Kyle Sinckler (Harlequins)
4 Dominic Barrow (Leeds Carnegie)
5 George Merrick (Harlequins)
6 David Sisi (London Irish)
7 Chris Walker (Leeds Carnegie) (C)
8 Jack Clifford (Harlequins)
16 Nathan Morris (London Wasps) on for Koree Britton 60 mins
17 Luke Cowan-Dickie (Exeter Chiefs) on for Alec Hepburn 60 mins
18 Ross Harrison (Sale Sharks) on for Kyle Sinckler 45 mins
19 Ben Nutley (Northampton) on for David Sisi 52 mins
20 Billy Vunipola (London Wasps) on for George Merrick 58 mins
21 Ben Spencer (Saracens)
22 Henry Slade (Exeter Chiefs)
23 Tommy Bell (London Wasps) on for Charlie Walker 60 mins
Content courtesy of RFU