Competitions
There are lots of competitions out there, some with a really wide choice of categories to enter and others very specific to year groups or subjects. These first ones are national or international competitions; scroll down for ones run by universities and summer schools. Check out the Awards page for even more ideas!
STEM Competitions
https://www.thebigbang.org.uk/the-big-bang-competition/
https://www.makeablechallenge.com/
https://triumphdesignawards.co.uk/
https://bieacompetition.org.uk/ (British International Education Association STEM Competition)
https://iymc.info/en/ (International Youth Math Challenge)
https://isaacphysics.org/ (problem solving competition)
https://oxsci.org/schools/ (essay competition)
https://rgs.org/schools/competitions (Royal Geographical Society competition; fixed number of entries per school so you'll need your teachers to get involved)
https://persecoding.net/ (for students in years 7-11 working in teams; Jan - March)
https://www.bebras.uk/ (computing challenge run by the Raspberry Pi foundation; held in November)
Girls only:
http://www.girlsthreeminutescience.org/ (you have 3 mins to get your message across! 1 Jan deadline)
https://www.ncsc.gov.uk/cyberfirst/girls-competition
Organisations including National Grid, BP, Shell often run competitions for schools; you'll need to search on their company websites for current opportunities.
There are also Physics, Maths, Chemistry, Biology and Informatics Olympiads which you enter via school.
CREATIVE Competitions
https://youngartists.royalacademy.org.uk/ (fine art)
https://www.ippawards.com/the-competition/ (photography)
https://slam.poetrysociety.org.uk/ (poetry)
https://poetrysociety.org.uk/competitions/foyle-young-poets-of-the-year-award/ (poetry)
http://ygd.bafta.org/competition (Game Design competition)
http://baftakids.org/competitions (Presenter competition)
bbc.co.uk/nssa (BBC Young Writers’ Award with Cambridge University invites young people in the UK aged between 14 -18 years to submit short stories of up to 1,000 words)
www.bbc.co.uk/youngcomposer (national competition, submissions due in June each year)
BUSINESS Competitions
www.res.org.uk/education/young-economist-of-the-year (Royal Economic Society Essay competition; July deadline)
https://iea.org.uk/essay-competition/ (Institute of Economic Affairs essay competition, Dec deadline)
www.10xchallenge.org.uk - (start with £10 and make a profitable business in 4 weeks)
www.young-enterprise.org.uk - (run a business for a year under the guidance of a volunteer)
OTHER Competitions
https://www.royalcwsociety.org/essay-competition (essay competition from the Commonwealth Society)
https://www.esu.org/competitions/psc/ (Debating competition; must apply through your school)
https://www.rotarygbi.org/projects/young-people/competitions/ (including categories such as Peacemaker, Chef, Artist, Photographer, Filmmaker, Writer, Environmentalist)
These academic institutions run essay competitions for interested students; check their websites for entry details and entry deadlines, which are typically Jan - April (you may need to search their websites if they update their webpages for the latest competition). The university competitions are mainly aimed at 6th form students.
https://www.sheffield.ac.uk/philosophy/events/essay-competition
https://www.nchlondon.ac.uk/essay-faq/
Oxford Colleges and Departments:
https://www.st-hughs.ox.ac.uk/prospective-students/outreach-at-st-hughs/ (History and Classics competitions)
https://www.chch.ox.ac.uk/research-and-academia/enter-tower-poetry-competition (sixth form only)
https://www.mod-langs.ox.ac.uk/schools/language-competitions (French, German, Spanish competitions, all age groups)
https://www.oriel.ox.ac.uk/study-us/schools-liaison/lloyd-davies-philosophy-prize (sixth form only)
https://clasoutreach.web.ox.ac.uk/competitions (competitions run by the Classics department at Oxford)
Cambridge Colleges and Departments:
https://www.girton.cam.ac.uk/humanities-writing-competition
https://www.fitz.cam.ac.uk/admissions/undergraduate-admissions/opportunities-prospective-applicants/essay-competitions (competitions for 6th form students in a range of subjects including architecture, land economy, medieval world, ancient world and classics, history)
https://www.pet.cam.ac.uk/essay-prizes
https://www.trin.cam.ac.uk/undergraduate/essay-prizes/ (6th form competitions in English Literature, Linguistics, Philosophy, History, Law and Politics)
https://www.newn.cam.ac.uk/admissions/undergraduates/newnham-essay-prizes/
Queens' College Estelle Prize of £500 for Year 12 English students
A number of commercial summer schools and organisations run competitions; check their websites for essay requirements and entry deadlines, which are typically March - June.
www.johnlockeinstitute.com/essay-competition
www.libraeducation.co.uk/essay-prize
www.immerse.education/essay-competition/
https://www.exponentialminds.academy/exponential-minds-competition