This information is not collected centrally.
However, under Part 2 of the Sexual Offences Act 2003, those convicted, cautioned or subject to a finding for relevant sexual offences are, subject to any sentencing threshold being met, required to notify the police of certain personal data at specified intervals; this requirement is colloquially known as "being on the sex offenders register".
One of the pieces of information that an offender is required to furnish is the address of their sole or main residence in the United Kingdom. Where the offender has no such residence (i.e. is homeless), they are required to provide the details of a place or places where they can regularly be found.
The wording in the 2003 Act amended the original requirement from the Sex Offenders Act 1997 which was that an offender without a permanent home should notify the details of a place that he regularly "visited". Offenders cannot register "no fixed abode" as their address and have not been able to do so since September 1997, when the 1997 Act came into force.
Additionally, sex offenders subject to notification requirements will be monitored by the police in the community, through the multi-agency public protection arrangements.