Flight
England has a number of airports, but the best option for most international travelers would be London Heathrow Airport. It is the busiest in the country with the easiest access to trains, buses, and rental vehicles.
Travel Note
From your airport destination, you can make your way down to the South coast by train, bus, or rental vehicle. If you'd like to travel by train down to Bournemouth, more information can be found here: https://www.thetrainline.com/train-times/heathrow-airport-(any)-to-poole If you'd like to travel by bus, more information can be found here: http://www.nationalexpress.com