Get rid of old card before applying for new?

I have 2 credit cards – Halifax Clarity and TSB both with approx. £6,000 limit. They are both cleared every month. I would like to get a purchases card in order to leave my money in the bank for longer such as the Virgin Money card with 30 months interest free. I applied for a Sainsbury’s card last year and they only offered me a £1,000 limit which I declined.

Would I stand a better chance of getting a new card with a higher limit if I were to close the TSB card first? I would like to keep the Halifax card for use abroad.

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