There are loads of motorcycle courier firms in London. (It's almost impossible to cross the road without getting knocked down by someone trying to ride a bike and read a map at the same time!). If you live in, or near London, just watch the Evening Standard for ads. (There are always vacancies).
The reason that there are so many firms in London, though, is because lots of companies want to get documents across the city fast. This, in turn, is because so many companies have their headquarters in London and most government departments are also in the capital. Outside of London, the picture changes dramatically. A few other big cities (notably Birmingham) may have a relatively small number of couriers operating in their area. Away from the big cities, however, motorcycle couriers are almost unknown. (What courier work there is is usually undertaken by taxi drivers. Away from the congested traffic of London, taxis can do the work just as cheaply as couriers and there isn't the constant flow of work to support couriers anyway).
So, if you're nowhere near London (or possibly Birmingham), you might find it difficult to get employment. (Look under 'couriers' in your local Yellow Pages to see if you can find any firms or ask at the local Job Centre if they ever have these sort of vacancies).
If you do manage to find a firm to take you on - and you're riding your own bike - you'll need to take great care to check on the position regarding insurance.
Happy biking!
Chris