You would need to consult the bye-laws of the relevant local authority. For example, Lewisham includes this provision:
"No person shall in the ground, after being requested to desist by an officer of the Council, or by any person annoyed or disturbed, or by any person acting on his behalf:
(a) by shouting or singing;
(b) by playing on a musical instrument; or
(c) by operating or permitting to be operated any radio, gramophone, amplifier, tape recorder or similar instrument;
cause or permit to be made any noise which is so loud or so continuous or repeated as to give reasonable cause for annoyance to other persons in the ground."
http://www.lewisham.gov.uk/NR/rdonlyres/C3E3DA BE-C43A-4C0D-8FD8-58C0B6AB355B/0/NewParksByela wsFeb2004.pdf
Bexley has no such provision but you might fall foul of the rules on 'erecting tents, booths, etc':
http://www.bexley.gov.uk/service/parks/byelaws .html
In the Royal Parks, you need the Secretary of State's permission to do just about anything ;-)
http://www.opsi.gov.uk/si/si1997/19971639.htm
Chris