There has always been extensive organized crime in England. However, since England has always been relatively economically successful, there has never been massive immigration out of England (at least in the past 100 years or so)

Italian organized crime (along with Russian, dominican, Irish, Nigerian, etc) generally proliferates by following existing, law abiding migration routes.

Conversely, British mobsters largely stayed in Britain. Among native, white British gangsters the east London based Kray brothers are infamous and representative of a very common type of cockney mobsters who got very busy in the mid-late 20th century.

More recently, “county lines gangs” are making a lot of money. These gangs are generally based out of London and buy drugs there and use the county train lines (commuter rail basically) to move the dope to smaller towns where it sells for more money. These gang members are often second-third generation immigrants, but they are solidly British.

There are also extensive foreign based organized crime groups operating all over England. Italian, west African, Caribbean, Eastern European, and south Asian organized crime groups have all spent literal generations building networks in Britain. Some of these groups have adopted a very British character over the years.