UK Residence
Visas that let you remain in the UK free of immigration restrictions, including British Citizenship
UK Permanent Residence and British Citizenship
After a suitable qualifying period of time has been spent in the UK you should be able to qualify for Indefinite Leave to Remain.
This is also known as ILR, Permanent Residence or Settled Status, depending on the method of qualification.
Once you are a Permanent Resident you are free of immigration restrictions and on your way to qualifying for British Citizenship.
Further information can be found below but get in touch if you would like to discuss your situation in detail.

British Citizenship
How to qualify for British Citizenship

Long Residence ILR
Indefinite Leave to Remain based on Long Residence when you have lived in the UK for 10 years with valid visas.

Indefinite Leave to Remain: Work Route
Indefinite Leave to Remain (ILR) for those in the UK with qualifying work and business visas

Indefinite Leave to Remain: Family Route
Indefinite Leave To Remain (ILR) For Those In The UK With Qualifying Family & Partner Visas