Want to hire a private jet at short notice, buy a rare blue diamond or pay a brass band to serenade your sweetheart? These are the sort of requests you can expect to be fulfilled if you own one of the UK’s most exclusive plastic cards. But don’t expect it to be gold or platinum. The card that signals you have arrived nowadays is more likely to be purple or black. And you have to be seriously wealthy to qualify – or even have to wait until you’re invited to apply.

Arguably, the purple Coutts World Card is the UK’s most exclusive. It is specially designed by Oswald Boeteng, the celebrity tailor, and can be yours if you have a Coutts current account. Sounds easy, but you must have £500,000 of liquid assets to invest.

The bank says the 23,000 people who have their World Card are expected to pay off their balance each month, as it is a charge rather than a credit card. Its annual fee of £350 is waived if you spend more than £50,000 a year, which more than half of Coutts clients do.

The free perks are enviable: access to a concierge service – a team of “lifestyle managers” – who will help to run all the cardholder’s social and leisure arrangements, including, for example, finding an Indian elephant for a wedding in Lewisham, southeast London. Cardholders also receive free annual travel insurance and a priority pass to executive airport lounges worldwide.

Similar benefits are offered by the American Express Centurion black card which, the company claims, is “the world’s most exclusive card . . . designed to meet the needs of the super-affluent”. But there is a catch. Money alone cannot guarantee you the shiny black card. Instead you must wait to be invited to apply. Gail Hodges, the director of UK premium cards at American Express, explains: “A select group of our members, who are high spenders and regular users of the benefits that American Express offers, are invited to hold the Centurion card.” They face a stiff charge of £650 a year for the privilege.

If you prefer credit to charge cards, the high street banks offer black credit cards, plus perks, if you manage to fall into the “high net worth” category.

At Lloyds TSB, for example, private banking clients who earn at least £250,000, or who have more than £250,000 of savings and investments, are eligible for its Private Banking American Express credit card which costs £250 a year. The interest rate is a modest 10.4 per cent, but once the annual fee is included, the APR rises to 45.2 per cent. Customers have free access to a concierge service which would normally cost £120 a month.

NatWest and Royal Bank of Scotland charge 11.2 per cent on their black credit card, which also offers concierge services, for those who earn at least £75,000 a year. Include the £250 annual charge, however, and the effective rate rises to a staggering 50.3 per cent.

At Barclays and HSBC, the perks are more limited. Barclays has two black cards. Customers who earn at least £100,000 can have the Infinite card, which provides travel insurance and access to concierge services, but only allows six visits a year to an airport lounge. The annual fee is £150.

Customers of Barclays Private Bank who have at least £500,000 of assets, get a black charge card at no extra charge, but there are no free perks.

HSBC’s indigo Premier card includes annual travel insurance and other travel perks, but no airport lounge access or concierge service.

One of the most accessible of the “exclusive” cards – which carries all the perks – is probably the i24 card, formerly known as the Morgan Stanley card, part of Goldfish. To qualify, you need to have an annual income of £50,000 or more, and pay a £275 fee. You will get annual travel insurance, executive airport lounge access and a concierge service. The interest rate for purchases is a competitive 13.9 per cent but, with the annual charge, it works out at 57.8 per cent. However, the card also offers 1 per cent cashback. Last year, the average monthly spend was £3,506, which means cardholders got £420 in cashbacks – far exceeding the annual fee.

What you don’t get with i24, though, is a black card. The colour is off-white – but off-white could turn out to be the new black.

Need assistance to run up your bill?

Even the wealthiest people may lack all the contacts for every whim. This is where the exclusive credit-card concierge services come in, for requests from restaurant bookings to the more esoteric, such as:

A “biography” written by a top author – this was arranged by one concierge service.

A discontinued design of wedding dress – it was sourced and shipped from Italy to the UK in time for the big day.

Champions League tickets – delivered to the customer outside a stadium in Spain.

Find earrings spotted on a trip to Venice – going on vaguely recalled directions, the shop was found, the purchase made and delivery arranged to the client.

An invitation to an exclusive Oscars after-party – access was arranged.

Instructions for tying a bow tie – a diagram was faxed and talked through by phone.

A specific model of Renault coupé not produced since 2003 – one concierge service located three of these rare cars in Europe.

Top tickets for a hit London theatre show needed urgently by a customer who had forgotten his wedding anniversary – booked.

Exclusive hospitality packages for Wimbledon, the Cannes Film Festival and the Monaco Grand Prix – all have been arranged.

CASE STUDY

Bob Kemp, 55, a commercial property manager and owner of Kemps Quay, a marina in Southampton, has had a Coutts World Card for the past five years. He says: “One of the great things about the card is that you can use it for large purchases and the transactions just go through without question.

“I am a modest collector of classic cars and have used it buy a £32,000 E-type Jaguar at auction. I also used it to pay for a 12-bore shotgun costing £19,000. When people see the Coutts World Card, they know you are credit-worthy.”

Mr Kemp has used the concierge service on several occasions too: “Mainly for arranging theatre and restaurant bookings at short notice, but another occasion was when I broke down in my car and had forgotten to take my AA details with me. I rang the concierge service and they contacted the AA on my behalf and got somebody out to me in about ten minutes.”

Mr Kemp, who is area chairman of the Lord’s Taverners, has also used his card when he is arranging charity events.