The Royal Navy currently possesses 20 Major Surface Combat Vessels, of which on average 5 are in refit at any one time. I very much doubt that the Royal Navy could put together 1 x Carrier Group (a carrier needs escorts) let alone 2.

At the strategic level the UK policy appears to be to make the Falklands issue one of self-determination, while at th same time making clear that the Falklands sovereignty issue is not linked to that of South Georgia, the South Sandwich Islands and the British 'slice' of Antarctica. If the Falkland Islanders did decide (or it was decided for them ) to join Argentina then valuable fishing and natural resource rights, as well as a claim to Antarctica would remain. I cannot help but wonder though, what would happen if the Falkland Islanders opted to join Chile instead...

Currently the Falklands are very prosperous with one of the highest per capita incomes in the Commonwealth and an enviable standard of living. The prosperity is based on incomes from fishing revenues. The commercial exploitation of oil and gas in territorial waters (including the claimed Exclusive Economic Zone - the EEZ) would be a strategic game changer for both the UK and Argentina.

One thing that the UK learnt very clearly from the 1982 conflict was the value of maybe having submarines in the area; I would expect this to continue.