Update 4 Aug 2015

The JMLSG has published new guidance which explicitly confirms (and clarifies) some of the information in this answer, specifically the sorts of tests a UK financial house needs to make on an individual. The new guidance (dated 14 Nov 2014) is at Guidance for the UK Financial Sector Part I.

The original answer does not need to be changed. New guidance only.

Original Answer

UK organizations that provide prepaid cards are regulated by the Financial Conduct Authority (formerly FSA), and the FCA places a very high priority on the prevention of money laundering. As a result, you will face several hurdles...

1. 18 years of age; and
2. Proof of identity; and
3. Resident in the UK

You can use your passport to establish items 1 and 2.

The third one may be a show-stopper for you. The interpretation of 'resident in the UK' is left to the organization itself. It's common that they will ask for a utility bill or bank statement that show your address along with the tenancy agreement from where you live. If you do not have those things, they will ask what you DO have. Some people newly arrived on a work permit bring a letter of introduction from their employer and this usually works. Otherwise if your evidence is insufficient, they will refuse to open an account or sell you a prepaid card (or face a penalty fine from the FCA).

Of course you are not intending to launder money, and your amount is probably insignificant, but rules are rules. There is no minimum amount before the rules are activated.

You have the same rigmarole if you try to rent a flat or hire a solicitor or pawn something and the list goes on.

There is nothing onerous about these requirements; native Brits have to comply with them also. Read the terms and conditions for the institution before wasting a lot of time on the application.

Finally, to locate organizations that provide prepaid credit cards, you Google on "prepaid credit cards in the UK". I found a suitable list at http://www.moneysupermarket.com/prepaid-cards/

You don't mention what country you are in, but Revolut could be an option for you.

It works as a pre-paid MasterCard debit card, which you can then recharge using their app (Apple and Android). The card is then usable pretty much anywhere in the world and purchases are made at Interbank rates, although the do make a small charge (2%) for most ATM withdraws.

They are UK based, but according to their FAQ, residents of most European countries can apply and get one, and as long as you can prove residency in one of the countries they deliver cards world wide.

From : https://revolut.com/faq/#where-is-revolut-available

Revolut is available to legal residents of the following countries:

Aland Islands, Austria, Azores, Belgium, Bulgaria, Canary Islands, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, French Guiana, Germany, Gibraltar, Greece, Guadeloupe, Hungary, Iceland, Ireland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Martinique, Mayotte, Netherlands, Norway, Poland, Portugal, Réunion, Romania, Saint Helena, Slovakia, Slovenia, Spain, St. Martin, Sweden, United Kingdom.

In the future we aim to become available worldwide!

Note I have no connection to Revolut other than being a happy customer.