Is it possible the destruction of tents in central London is legal?
Yes, it is possible the destruction of tents in central London is legal. There may be a legal justification that we are not aware of at the time of writing.
A possible legal justification:
In accordance with section 149 of the Highways Act 1980 the local authority might have issued a notice and successfully applied for a 'removal and disposal order'. Anecdotally that is not an uncommon procedure although I am unable to find statistics about it.
Removal of things so deposited on highways as to be a nuisance etc. s149 Highways Act 1980:
(1) If any thing is so deposited on a highway as to constitute a
nuisance, the highway authority for the highway may by notice require
the person who deposited it there to remove it forthwith and if he
fails to comply with the notice the authority may make a complaint to
a magistrates’ court for a removal and disposal order under this
section.
(2) If the highway authority for any highway have reasonable grounds
for considering—
(a) that any thing unlawfully deposited on the highway constitutes a
danger (including a danger caused by obstructing the view) to users of
the highway, and
(b) that the thing in question ought to be removed without the delay
involved in giving notice or obtaining a removal and disposal order
from a magistrates’ court under this section,
the authority may remove the thing forthwith.
(3) The highway authority by whom a thing is removed in pursuance of
subsection (2) above may either—
(a) recover from the person by whom it was deposited on the highway,
or from any person claiming to be entitled to it, any expenses
reasonably incurred by the authority in removing it, or
(b) make a complaint to a magistrates’ court for a disposal order
under this section.
(4) A magistrates’ court may, on a complaint made under this section,
make an order authorising the complainant authority—
(a) either to remove the thing in question and dispose of it or, as
the case may be, to dispose of the thing in question, and
(b) after payment out of any proceeds arising from the disposal of the
expenses incurred in the removal and disposal, to apply the balance,
if any, of the proceeds to the maintenance of highways maintainable at
the public expense by them.
(5) If the thing in question is not of sufficient value to defray the
expenses of removing it, the complainant authority may recover from
the person who deposited it on the highway the expenses, or the
balance of the expenses, reasonably incurred by them in removing it.
(6) A magistrates’ court composed of a single justice may hear a
complaint under this section.
Another possible legal justification:
Section 235 of the Local Government Act 1972 enables district and borough councils to make byelaws for the good rule and government of the whole or any part of the district or borough and for the prevention and suppression of nuisances.
Section 150(2) of the Police Reform and Social Responsibility Act
2011 amended the Local Government Act 1972 (offences against byelaws) to insert
237ZA Section 235 byelaws: powers of seizure etc
A byelaw made under section 235 may include provision for or in
connection with—
(a)the seizure and retention of any property in connection with any
contravention of the byelaw, and
(b)the forfeiture of any such property on a person's conviction of an
offence of contravention of the byelaw.
This enables local authorities to attach powers of seizure and retention
of any property (which could include tents and sleeping equipment) in
connection with any breach of a byelaw made under section 235 and
enables the courts to order forfeiture of any such property on conviction
for contravention of any byelaw.
The City of Westminster introduced such a byelaw in March 2012 in relation to tents and other sleeping equipment in and around Parliament Square. See City of Westminster - Parliament Square byelaws.
Reference for second justification: Department for Communities and Local Government - Dealing with illegal and unauthorised encampments. Focuses on 'travelers' but it is more broadly applicable.