Major difference if you are flying light aircraft for pleasure in IFR then you will not be in controlled airspace most of the time in the UK, whereaas in most parts of the US you are always in at least class E airspace.
Hence you are not under positive radar control and it is up to you to request radar services if they are available in the area.
If you require to enter airways then you need both a filed flight plan and an airborne clearance with details such as place and time of airway entry.
As you already fly VFR here then you will be familiar with most of the RT - there is not much more to learn under IFR here.
Good Luck