I believe its difficult to get to central london from gatwick airport and my time is limited in this city.
please advise the easiest way, without having to change over with luggage etc.
>I believe its difficult to get to central london from gatwick airport
But 'easiest, quickest and cheapest' never go together, anywhere.
The quickest option is to take the Gatwick Express train, the Gatwick Connect train is a bit cheaper and only a little slower and there are also other train options from the airport station. Use the official UK railway website to see details for all trains on the route for your date and preferred time: www.nationalrail.co.uk
Long-distance buses such as Easybus and National Express are cheaper but slower than taking the train. They can also get delayed by traffic congestion, which is a frequent occurrence on that route.
Taxis and pre-booked transfers are expensive. They can be quicker than buses because they can change routes but they won't be as fast as the train.
Note that if you take either train or bus you may still have to change to other transport (Tube, bus, taxi) on arrival in London. It all depends on where you are staying.
Mentioned in this answer:
Getting to central London from Gatwick is easy. I took the non-stop Gatwick Express. It was only a 30-minute ride, and I agree with Courtney that it's the fastest from Gatwick to Victoria Station. You can explore the following trains to other London stations:
Take the easyBus or National Express to Victoria Coach Station if you prefer going on buses.It's the cheapest way. Here are the links:
National Express: http://www.nationalexpress.com/en/airports/gatwick-airport.aspx
Hope this info helps.
I've also taken the bus from there but it takes much, much longer--about an hour and a half as opposed to half an hour.