A lot of the sites I use for booking holidays are done independently and I find this is often a much cheaper way of travelling and it is not always necessary to go through a travel agent. Provided you have adequate travel insurance, these days there is no reason for concern. Many of the sites I recommend I have used for years without any issues so I am confident at giving you their details in the hope that you too will be looking at making savings on your next trip.
The first of my favourites is www.booking.com to book hotels and apartments. What I like about this site is that you know just where you stand with them. You know how many rooms they have left at the price stated. They will often do the same rate per room or sometimes slightly higher for free cancellation. I have travelled a number of times with friends who have had to cancel due to illness and being able to cancel last minute took a lot of stress away from the booking. There is a lot of choice available and the rates they offer are very competitive, often much cheaper than other sites. There are a lot of reviews to give you an informed choice about where to stay. Finally, if you use them regularly then you begin to be offered discounts off the prices they have on their website