Seems I am wrong about furious cycling after all - sorry! Bicycles are still not covered by speeding regulations (1984) which only deal with motorised vehicles.
Here is the full section of the Road Traffic Act 1988 applying to bicycles. What constitutes recklessness, carelessness or inconsiderate cycling would still be a judgement call by a police officer (and then later by a magistrate)... it would make sense to argue that cycling over the speed limit might indeed constitute an offence, but it can't be argued on the basis of the speed alone for cyclists.
RTA 1988 excerpt
Cycling offences and cycle racing
28 Reckless cycling A person who rides a cycle on a road recklessly is guilty of an offence.
In this section “road” includes a bridleway.
29 Careless, and inconsiderate, cycling If a person rides a cycle on a road without due care and attention, or without reasonable consideration for other persons using the road, he is guilty of an offence.
In this section “road” includes a bridleway.
30 Cycling when under influence of drink or drugs (1) A person who, when riding a cycle on a road or other public place, is unfit to ride through drink or drugs (that is to say, is under the influence of drink or a drug to such an extent as to be incapable of having proper control of the cycle) is guilty of an offence.
(2) In Scotland a constable may arrest without warrant a person committing an offence under this section.
(3) In this section “road” includes a bridleway.
31 Regulation of cycle racing on public ways (1) A person who promotes or takes part in a race or trial of speed on a public way between cycles is guilty of an offence, unless the race or trial—
(a) is authorised, and
(

is conducted in accordance with any conditions imposed,
by or under regulations under this section.
(2) The Secretary of State may by regulations authorise, or provide for authorising, for the purposes of subsection (1) above, the holding on a public way other than a bridleway—
(a) of races or trials of speed of any class or description, or
(

of a particular race or trial of speed,
in such cases as may be prescribed and subject to such conditions as may be imposed by or under the regulations.
(3) Regulations under this section may—
(a) prescribe the procedure to be followed, and the particulars to be given, in connection with applications for authorisation under the regulations, and
(B) make different provision for different classes or descriptions of race or trial.
(4) Without prejudice to any other powers exercisable in that behalf, the chief officer of police may give directions with respect to the movement of, or the route to be followed by, vehicular traffic during any period, being directions which it is necessary or expedient to give in relation to that period to prevent or mitigate—
(a) congestion or obstruction of traffic, or
(B) danger to or from traffic,
in consequence of the holding of a race or trial of speed authorised by or under regulations under this section.
(5) Directions under subsection (4) above may include a direction that any road or part of a road specified in the direction shall be closed during the period to vehicles or to vehicles of a class so specified.
(6) In this section “public way” means, in England and Wales, a public highway and, in Scotland, a public road and includes a bridleway but not a footpath.
32 Electrically assisted pedal cycles (1) An electrically assisted pedal cycle of a class specified in regulations made for the purposes of section 189 of this Act and section 140 of the [1984 c. 27.] Road Traffic Regulation Act 1984 shall not be driven on a road by a person under the age of fourteen.
(2) A person who—
(a) drives such a pedal cycle, or
(B) knowing or suspecting that another person is under the age of fourteen, causes or permits him to drive such a pedal cycle,
in contravention of subsection (1) above is guilty of an offence.