I am well aware that there was a settlement in Uxbridge long before the late 19th / early 20th century but what really brought it to where it is now was the development of the Railway which metamorphosed into the Tube (Underground / subway) over time. Uxbridge is now well-served for Tube services being a terminus station on both the Metropolitan and Piccadilly Lines (purple and dark blue respectively on your Tube map) and the station is in Zone 6 if you are wondering about getting the correct ticket. Typical travel times from central London are about an hour direct on the Piccadilly line from Leicester Square and about 40 minutes from Baker Street on the Metropolitan Line.
I should add that the Metropolitan Line has recently introduced some new rolling stock (pictured) which makes for a very pleasant journey. As with any London public transport, do try and avoid rush hours. I do recommend the attached official Government website for planning any public transport journey in London.
The London Underground services of Piccadilly and Metropolitan lines terminate at Uxbridge Station. This is located in the heart of the town centre and immediately next to it is the bus station/terminus.
The buses take you further into the London Borough of Hillingdon, Buckinghamshire, Ealing, Southall and so on. The buses also travel to main rail links such as Hayes & Harlington, West Drayton and West Ruislip to name but three.
The A10 and U3 services travel to Heathrow Central bus terminus and then from there onwards to anyweher in world!
Uxbridge lies just inside the M25, and gives the appearance of a medium sized provincial town. Except that is for one vital difference - it lies right on the end of the Metropolitan and Piccadilly tube lines. As such it is very easily connected to central London. And Acton.