I don't see a way back for England really. If they went to Perth at 1-1, i could see them maybe finding a way to leave here with a 2-2 result but that won't happen now. For it's nuances and talk about tactics, follow ons and declarations, cricket's a simple game. England haven't made enough runs, conceded too many and been unable to turn good positions into dominant positions.
In Brisbane, they scored 302 batting first, a total i'd say 80+ short of what was needed. When Australia was batting, they had then 4-76 and instead of a first innings lead of 60+, Australia ended up with a first innings lead. failure to get over 200 in their second innings meant the game was gone unless Australia put on an embarrassing collapse which didn't happen. A first innings lead of 60 and a total of 280 or so in their 2nd dig and they set Australia a challenging total. Instead it was a procession for Australia.
In Adelaide, Root's decision to bowl first might have ended up being vindicated. Early on day two, they Australia 5-209. Bowl well, and they could have bowled Australia out for not much more than 300. As it was, Australia made 442. 227 from England in reply, wasn't enough. At least 100 short in my opinion. Yes, they bowled well in Australia's 2nd innings, but i'd suggest the damage was done. Having set England 354 to win, i was always confident Australia would win. Stubborn South African batting line ups in a day time test might have been able to bat long enough to chase that down but this England team are incapable of batting long enough to make enough runs when they bat.
No point now in playing Ben Stokes either to be honest. If it was 1-1 heading to Perth, i could see sense in playing him if he was in the right frame of mind. Not now, though as England will lose the series with or without Stokes, potentially 5-0 too. They don't need the media storm that will come with Stokes playing when they're likely to lose badly.
Also Matt Prior, put up or shut up.