If you want my opinion I think we need a temporary coalition Government probably led by Jeremy Hunt as rep of the party with most MPs who came second place in last year’s leadership contest and has health experience. Starmer deputy, reps from SNP, Plaid, DUP all in the Cabinet. Rest of the Government made up of competent MPs from across Parliament.
Oh that that would happen!! However it won't because of the adversarial nature of our system.
It might however be worthwhile having a cross party committee, made up of all the main players you named to coordinate covid-19 response across the UK; but WITHOUT England (that is the British government) having a veto over decisions it didn't like. Again, sadly, because of our broken system, probably won't happen.