Are you asking whether or not the UKBA maintains records of all persons coming to the UK under immigration law and also whether they track their movements in and out of the country?
For what purpose do you wish to know?
What is the person's immigration status and position?
Yes, the UKBA has a centralised system. Your entry in to the country and travels thereafter would be stamped in your passport each time you pass through UK customs. This would then be noted on the UKBA's system.
Even if they made an error and did not check their system when you make an application for a different visa/renewal you would have to submit your passport and this would obviously contain the stamps at customs so this is another way they could check your arrival and time out of the country.
They would then compare this to appropriate eligibility criteria for the application you are making and against your statements to check that it tallies and that there are no inconsistencies which may speak to dishonesty.
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