My scenario - What do you think?

marathonic

If you must have the home improvements as soon as possiible, how about:

• Pay off credit card with savings;
• Close it;
• Save £2,000 whilst your credit file updates with the fact that the card has been settled and is closed;
• Apply for a £3,000 credit card with interest free purchases for a certain time period
• Do your £5,000 home improvements with the credit card and £2,000 savings

If you don't get approved for the £3,000 card, just continue saving (if you can hold off long enough, it'd be better to do this in the first place).