I think that you will find that the training system works differently in the UK to how it works in Australia and the USA. Trainers do not train at the racecourses themselves, although several of our big racehorse training areas are associated with local racecourses.
The town of Newmarket has two racecourses and a large number of the biggest names in the training business are based there; however, much of the land in the area that is not actually the racetracks is taken up with gallops that are maintained collectively for the trainers to use.
The two other big areas are at Lambourn, which is geographically West of London near to Newbury racecourse; and Malton, which is North East of the city of York.
A couple of places that spring to mind as having quite a few trainers nearby are Middleham in North Yorkshire and Epsom (home of The Derby) in Surrey.
There are plenty of trainers scattered all over the country, especially in the National Hunt game where there are many smaller yards.
If you go onto Google maps and type in one of the locations so that it shows you a map and then type in “horse trainers locations” it should add lots of dots to the map showing you various training establishments. Hold the cursor over a dot and it should tell you the trainer.
In terms of a website where you can find details of trainers and their locations individually, you might try
http://www.racing-index.com/horseracing/trainers/.