Noise can be annoying, distracting, frustrating and - particularly when it results in lack of sleep - it can be prejudicial to health. Having suffered it myself, I have every sympathy for people in similar circumstances who want to take a bat to the infernal noisemaking device.
However, there seems to be nothing Bob himself can lawfully do directly to the burglar alarm itself.
It is unlawful for Bob to without authorisation enter the land or premises (trespass to land), interfere with the alarm (trespass to goods) or damage the alarm (trespass to goods and/or section 1 Criminal Damage Act 1971).
Bob should call the local authority's environmental health department.
Bob should ask if the premises is within a designated 'alarm notification area' per the Clean Neighbourhoods and Environment Act 2005. If this is the case then the owner/occupier of the premises must have given the local authority the details of a 'nominated key-holder' to be contacted if the owner/occupier can't be contacted, so that the alarm can be silenced. It is an offence for the owner/occupier to not do that.
Also, Sections 77 to 79 of the Clean Neighbourhoods and Environment Act 2005 create powers in relation to audible intruder alarms. An "authorised officer of the local authority" can enter land to disable an external alarm or seek a warrant to enter premises to disable an internal alarm.
(2) The conditions are—
(a) that the alarm has been sounding continuously for more than twenty
minutes or intermittently for more than one hour;
(b) that the sounding of the alarm is likely to give persons living or
working in the vicinity of the premises reasonable cause for
(c) if the premises are in an alarm notification area, that reasonable
steps have been taken to get the nominated key-holder to silence the
In addition, among other things, Part III of the Environmental Protection Act 1990 makes it a duty of every local authority to take reasonable steps to investigate complaints of noise nuisance to decide if there is a 'statutory nuisance'. If there is a statutory nuisance then the local authority must serve an 'abatement notice'. A criminal offence is committed if the statutory nuisance is not abated. No help in the short-term, but it is another lawful avenue.
The more neighbours who complain, the more inclined the local authority may be to intervene sooner rather than later. It is lawful for Bob to tell neighbours about these parts of the Clean Neighbourhoods and Environment Act 2005 and the Environmental Protection Act 1990 and suggest they complain too, and/or prime them for visits from an investigator.