Some readers may like to give money to homeless people - a kind and generous gesture. In London (and most big European cities), it is also a foolish one. Beggars are often victims of human trafficking, or part of a begging "ring" where they must give a cut, or all, of their "earnings" to someone else. As a result, the money you thought would be helping them is not.
An even better reason not to give money to beggars: new police reports show growing numbers of beggars are not homeless (see link above). Yes, people actually beg professionally because they can make up to 200GBP a day, tax free. In this economy it is not suprising that more and more people are turning to the streets for money.
If you live in London and truly feel the need to help the homeless buy them something to eat (ask them first though because often they refuse even new food), or buy a copy of the Big Issue.
Keep your spare change, unless you are happy paying for someone to remodel their kitchen.
Note for visitors in London: The Big Issue is a magazine program which gives homeless people a product they can sell instead of begging. People you see performing inside London Underground stations (but not the ones that are actually riding on the tube), are not beggars. They have auditioned to play there and have permits. These people are professional buskers, not beggars and many of them are actually quite good.