Thatcher doing nothing means she's gone - and fast.
The Conservative poll position was recovering by 1982 but was still damn low and neck and neck with the Alliance. It should be remembered that Thatcher wasn't terribly popular with her Cabinet. Add to that accepting the loss of British citizens to a foriegn dictator, Tory support takes a dive as the Party revolts on the issue, Foot leads pro-war calls in Parliament and the Cabinet quickly play ip-dip-dip over who shanks Maggie and takes over.
Cue a hurried effort to retake the Islands, possibly ending in disaster due to delays/weather/stronger defences. Either that or they go through the UN and get a deal of some sort.
Conservatives hold out til 1984 for General Election. Economic upswing will help but the propaganda disaster of Thatcher's overthrow and the loss of the Falklands will do far more damage in return. Foot's "voice of sanity" during the crisis will be comended, so Labour will probably do a little better. However it will be the Alliance who gain the lion's share of defecting Tories.
In the end I dare say this will lead to a bloody mess. Labour will struggle even harder to outdo the Alliance proportionally, while the Alliance's new votes won't transfer into many new seats.
In the end you'll probably get a Conservative Government, its majority cut down to 20-25 seats and general sense of political malaise. Whoever took over from Thatcher will be secured by a win but I would be surprised if another coup took place, particularly depending how the Miner's Strike fares.
In Labour, Foot will go still but his better public image will probably focus blamers on the Manifesto, not the leader, possibly leading to a quicker reform of the Party.
In the Alliance, they'll be even more pissed about how nonsensical British Democracy works but I doubt it will change much for them.