What's best to do with unused credit cards?

MallyGirl

From that list I'd keep:

Barclaycard (2) 16,000
Halifax (2) 15,000 (Partner)

MBNA (2) 16,500
MBNA (3) 13,000 (Partner)

That gives long relationship, high limit cards, MBNA often do money transfer offers (one of the few that do), Barclaycard give offers if the card is being used.

Candyapple

matt8787
Barclaycard £8,900
Barclaycard £16,000
Halifax £9,600
Virgin £15,000
MBNA £7,000
MBNA £16,500
MBNA £6,000
Tesco £5,800
Total: £84,800

Partner
Nationwide £2,000
Tesco £5,400
Sainsburys £11,000
MBNA £13,000
Halifax £15,000
Total: £46,400

If I were in your shoes given the answers you have said, I would keep the oldest Barclaycard and close the other one.

Halifax - you're allowed 2 cards from Halifax so if you needed to apply for a new card you'd be ok.

Virgin - same as Halifax.

Tesco - same as Halifax.

MBNA - I would close 2 and keep 1.

So in total you end up with 5 cards instead of 8. It's up to you both whether you want to lower some of your limits, although I imagine you both have high salaries so wouldn't make that much of a difference if you want to apply for a new card in future.