with reference to online trading ,how long does it take an online
investor
to be able to sell his newly bought shares from the time his buy order
has been executed? in other words can i buy and sell the same
shares in a space of say 10 seconds,if the answer is yes could you
please direct me to an online broker who offers this service in the
United Kingdom at a competitive price (no more that £10 per trade).

Most online brokers won't guarantee times like that due to system and
internet delays. What you are talking about is generally referred to
as 'Day Trading'. Most major cities have facilities that accomodate
day traders, though they do charge fees and what not...

Hope that helps.

Here in the USA, most online brokers (Ameritrade is one) usually have
10-30 second order executions. I have a link for you, shop around, get
the best online broker, with the best pricing plan.
http://www.find.co.uk/advice/ASB/